Probability

Problem 1301

```latex \textbf{Problem:}
\begin{enumerate} \item[(A)] Eine Katze erwartet Drillinge. Die Wahrscheinlichkeit, dass ein Jungtier männlich wird, betrage 50\% (Modell Annahme, die näherungsweise stimmt). \item[(B)] Fassen Sie die Drillingsgeburt als Zufallsexperiment auf, simulieren Sie mit einer Münze oder einem elektronischen Gerät. \end{enumerate}

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Problem 1302

```latex Beim Lotto "6 aus 49" ist für die Zufallsgröße "Anzahl der richtigen pro Tipp" die Wahrscheinlichkeitsverteilung (gerundet) in der Tabelle angegeben:
rP(X=r)00,43610,41320,13230,017740,00096951,8510567,15108\begin{array}{c|c} r & P(X = r) \\ \hline 0 & 0,436 \\ 1 & 0,413 \\ 2 & 0,132 \\ 3 & 0,0177 \\ 4 & 0,000969 \\ 5 & 1,85 \cdot 10^{-5} \\ 6 & 7,15 \cdot 10^{-8} \\ \end{array}
\begin{enumerate} \item[(A)] Berechnen Sie den Erwartungswert und die Standardabweichung für die Anzahl der richtigen. \item[(B)] Kontrollieren Sie die Angaben für P(X=0) P(X = 0) , P(X=1) P(X = 1) und P(X=6) P(X = 6) mithilfe der Pfadregel. \end{enumerate} ```

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Problem 1303

```latex \begin{enumerate} \item[(A)] Aus einem Beutel mit zwölf 0,50 € Münzen, fünf 1 € Münzen und 82 2 € Münzen nimmt man zwei Münzen. Berechnen Sie den durchschnittlichen Geldbetrag, den man herausziehen wird, und die Standardabweichung der Geldbeträge. \item[(B)] Benennen Sie weitere Zufallsgrößen, die zu diesem Experiment passen könnten. \end{enumerate}

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Problem 1304

Roger Hunt intends to purchase one of two car dealerships currently for sale in a certain city. Records obtained from each of the two dealers reveal that their weekly volume of sales, with corresponding probabilities, are as follows. Dahl Motors Cars Sold/Week 5 6 7 8 9 10 11 12 Probability 0.05 0.09 0.14 0.24 0.18 0.14 0.11 0.05 Farthington Auto Sales Cars Sold/Week 5 6 7 8 9 10 Probability 0.08 0.21 0.31 0.24 0.10 0.06 The average profit per car at Dahl Motors is $543\$543, and the average profit per car at Farthington Auto Sales is $653\$653.
(a) Find the average number of cars sold each week at each dealership. Dahl cars Farthington cars
(b) If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase? (Compare the expected weekly profit for each dealership.) The expected weekly profit from Dahl Motors is $\$ . The expected weekly profit from Farthington Auto Sales is $\$ . Therefore, Roger should purchase --Select--- .

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Problem 1305

Die Zufallsgröße XX gibt den Gewinn in Euro bei einem Glücksspiel mit Einsatz von einem Euro an. Die Tabelle gibt ihre Wahrscheinlichkeitsverteilung an:
gP(X=g)WIN1291502151561545\begin{array}{c|c} g & P(X=g) \\ \hline \text{WIN} & \frac{1}{2} \\ \frac{9}{15} & 0 \\ \frac{2}{15} & \frac{1}{5} \\ \frac{6}{15} & \frac{4}{5} \\ \end{array}
A) Berechnen Sie den Erwartungswert und die Standardabweichung von XX.
B) Wie groß muss der Einsatz sein, damit das Spiel fair ist?
C) Ändern Sie die maximale Auszahlung so ab, dass das Spiel bei einem Einsatz von einem Euro fair ist.

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Problem 1306

Berechnen Sie für die Zufallsvariable X X mit der Wahrscheinlichkeitsverteilung in der Tabelle den Erwartungswert und die Standardabweichung.
P(X=k)k5%220%140%435%7\begin{array}{c|c} P(X=k) & k \\ \hline 5\% & 2 \\ 20\% & 1 \\ 40\% & 4 \\ 35\% & 7 \\ \end{array}

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Problem 1307

```latex \text{Berechnen Sie die folgenden Wahrscheinlichkeiten für eine binomialverteilte Zufallsgröße } X \text{ mit den Parametern:}
\begin{itemize} \item \text{A) } n = 50 \text{ und } p = 0,05 \item \text{B) } n = 100 \text{ und } p = 0,03 \end{itemize}
\begin{align*} &P(X = 4) \\ &P(X < 4) \\ &P(X > 3) \\ &P(1 < X < 5) \\ &P(X < 1 \text{ oder } X < 5) \end{align*} ```

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Problem 1308

2 Etwa 20% der Deutschen sind blond. Wie groß ist die Wahrscheinlichkeit, dass in einer Schulklasse mit 25 Schülerinnen und Schülern a) genau 5 blond sind? b) zwischen 4 und 6 c) höchstens 5 d) mindestens 6 e) Wie viele Blonde erwarten Sie nach der obigen Information in Ihrem Kurs? Prüfen Sie, ob die tatsächliche Anzahl im 2σ-Intervall um den Erwartungswert liegt.

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Problem 1309

7 Eine Zufallsgröße XX ist binomialverteilt mit den Parametern n=15n = 15 und p=0,2p = 0,2.
a) Bestimmen Sie P(X=4)P(X = 4) und P(X4)P(X \le 4).
b) Erklären Sie, wieso man P(X3)P(X \ge 3) mithilfe des Terms 1P(X2)1 - P(X \le 2) berechnen kann.
c) Bestimmen Sie P(1X5)P(1 \le X \le 5).

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Problem 1310

8 Der Wochenspiegel ist eine kostenlose Werbezeitung mit einer Auflage von 5000 Exemplaren. In 80% aller Haushalte wandert sie ungeöffnet in die Mülltonne. Wie hoch ist die Wahrscheinlichkeit, dass a) höchstens 980 b) mindestens 1100 Exemplare gelesen werden? c) Schätzen Sie mit der 2σ-Regel, in welchem Intervall die Anzahl gelesener Exemplare mit ca. 95,4%-iger Wahrscheinlichkeit liegt.

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Problem 1311

1 Aus der Prüfstatistik eines Kugelschreiberherstellers geht hervor, dass 3%3\% der produzierten Kugelschreiber defekt sind. Mit welcher Wahrscheinlichkeit a) ist von 15 Kugelschreibern keiner defekt, b) sind von 25 Kugelschreibern mindestens zwei defekt, c) sind von 50 Kugelschreibern höchstens zwei defekt, d) beträgt die Anzahl von defekten bei 100 Kugelschreibern mindestens 2 und höchstens 4? P bestimmen, entscheiden

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Problem 1312

3 a) Ein Blumenzüchter gibt auf seine Zwiebeln eine Keimgarantie von 95%95\%. Falls in einer Stichprobe von 100100 Zwiebeln nur 9090 oder weniger aufblühen, braucht ein Gartencenter die Lieferung nicht zu bezahlen. Berechnen Sie die Wahrscheinlichkeit, dass das Gartencenter eine Lieferung, die den Angaben des Blumenzüchters entspricht, umsonst erhält. b) Mit welcher Wahrscheinlichkeit war sogar noch mehr als ein Platz übrig? b) Berechnen Sie die Wahrscheinlichkeit, dass das Gartencenter eine Lieferung bezahlt, bei der die Keimwahrscheinlichkeit tatsächlich nur 85%85\% beträgt.

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Problem 1313

4 Die Wahrscheinlichkeit einer Jungengeburt beträgt ca. 50%. Wie groß ist die Wahrscheinlichkeit, dass in einer Woche mehr als 55% der Neugeborenen männlich sind? Schätzen Sie zuerst. a) In einem Ort mit wöchentlich 50 Geburten. b) In einer Stadt mit wöchentlich 400 Geburten.

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Problem 1314

7 Wie oft muss man mindestens würfeln, damit mit einer Wahrscheinlichkeit von mindestens 99% das angegebene Ereignis erzielt wird? a) eine Sechs b) eine Primzahl c) zwei gerade Zahlen d) drei Zahlen unter 6

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Problem 1315

10 Die Wahrscheinlichkeit für die Geburt eines Jungen beträgt etwa 0.50.5.
a) In einem Jahr werden in einer Kleinstadt 100100 Kinder geboren. Berechnen Sie die Wahrscheinlichkeit, dass mindestens 5050 Jungen geboren werden. Berechnen Sie die Wahrscheinlichkeit, dass die Zahl der Jungengeburten mindestens 4545 und höchstens 5555 beträgt.
b) Wie viele Kinder müssen mindestens geboren werden, damit mit einer Wahrscheinlichkeit von mindestens 9999% mindestens ein Junge dabei ist?

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Problem 1316

11) Über einen Nachrichtenkanal werden Zeichen übertragen. Durch Störeinflüsse wird jedes Zeichen mit der unbekannten Wahrscheinlichkeit pp falsch übertragen. Die Störung der einzelnen Zeichen erfolgt unabhängig voneinander. Wie groß darf pp höchstens sein, wenn die Wahrscheinlichkeit, dass bei 100 übertragenen Zeichen mehr als eines falsch übertragen wird, höchstens 10% betragen darf?

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Problem 1317

Find the probability of at least one girl in 9 births, given boy probability is 0.521. Round to three decimal places.

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Problem 1318

In a country with a boy birth probability of 0.509, find the chance of at least one girl in six births using P(A)=1P(Aˉ)P(A)=1-P(\bar{A}).

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Problem 1319

What is the probability of at least one girl in six births if the chance of a boy is 0.509?

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Problem 1320

In an experiment, students received either 4 quarters or a \$1 bill. Find the probability a student spent money given they got quarters.

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Problem 1321

In an experiment, students received either four quarters or a \$1 bill. Find the probability of a student spending money given they got quarters.

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Problem 1322

In an experiment, find the probability a student with four quarters spent money on gum. Round to three decimal places.

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Problem 1323

In an experiment, students received either four quarters or a \$1 bill. Calculate the probabilities of spending or keeping money.
a. Probability of spending given four quarters is 0.745. b. Find the probability of keeping money given four quarters.

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Problem 1324

In an experiment, find the probability that a student who got a \$1 bill spent it on gum. Round to three decimal places.

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Problem 1325

In an experiment, students received either four quarters or a \$1 bill. Calculate the probabilities for parts (a) and (b) below.
a. Find the probability a student spent money given they received a \$1 bill.
b. Find the probability a student kept money given they received a \$1 bill.

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Problem 1326

Given a 6%6\% disk drive failure rate, find the probability of avoiding data loss with 2 and 3 drives. Round to four decimal places.

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Problem 1327

Given a 6%6\% disk drive failure rate, find the probability of having at least one working drive with 2 and 3 drives.

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Problem 1328

Find the positive predictive value of a polygraph test: P(Lied | Positive) using the data: 13 No, 45 Yes, 30 No, 12 Yes.

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Problem 1329

Given a 6%6\% disk drive failure rate, find the probability of at least one working drive:
a. For 2 drives: 0.9964 b. For 3 drives: (calculate and round to six decimal places)

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Problem 1330

Find the probability of a positive result when combining two samples, given a 0.2 probability of a positive test. Round to three decimal places.

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Problem 1331

Find the probability of a positive test for two combined samples, given a single sample has a 0.2 chance. Result: 0.36. Is further testing needed? A. Yes, B. No, C. Always, D. Never.

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Problem 1332

Translate P(BA)\mathrm{P}(\mathrm{B} \mid \mathrm{A}) into words: probability polygraph indicates lying if subject tells the truth. Choose the correct option.

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Problem 1333

Find the probability that at least one of seven randomly selected births is a boy, given the girl probability is 0.482. Round to three decimal places.

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Problem 1334

Find the probabilities for a 52-card deck: a. Probability of one suit. b. Face card then numbered card. c. One suit then face card.

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Problem 1335

Find the probabilities using a 52-card deck. Provide answers as reduced fractions.
a. Probability of drawing any one suit (diamond, heart, spade, club)? b. Probability of drawing a face card first, then a numbered card? c. Probability of drawing any one suit first, then a face card?

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Problem 1336

Find the probabilities using a 52-card deck: a. Probability of drawing one suit. b. Probability of face card then numbered card. c. Probability of one suit then face card. Assume no replacement.

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Problem 1337

Find the probabilities using a 52-card deck. Reduce your answers to fractions.
a. Probability of drawing a diamond: P(D)=1352P(D) = \frac{13}{52}.
b. Probability of drawing a king then a 2: P(K,2)=452451P(K, 2) = \frac{4}{52} \cdot \frac{4}{51}.
c. Probability of drawing a heart then a queen: P(H,Q)=1352451P(H, Q) = \frac{13}{52} \cdot \frac{4}{51}.

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Problem 1338

Find the probability of picking a red marble from 10 total marbles: 6 red, 1 purple, 3 green. Give answers as a decimal and percentage.

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Problem 1339

Find the probabilities using a 52-card deck: a) P(diamond), b) P(king then 2), c) P(heart then queen). Reduce fractions.

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Problem 1340

If P(A)=0.95\mathrm{P}(\mathrm{A})=0.95, what does this mean? Choose the best interpretation. 10 points. A, B, C, or D?

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Problem 1341

What does P(A)=0.32\mathrm{P}(\mathrm{A})=0.32 mean? Choose one: A. unlikely, B. less often, C. never, D. always.

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Problem 1342

What is the probability that a randomly selected student from 65 in a Film Production course is a Senior?

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Problem 1343

What is the empirical probability that Joan rolls a 4 after rolling a fair four-sided die 37 times and getting 4 five times? A. 5%5 \% B. 37%37 \% C. 25%25 \% D. 13.51%13.51 \%

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Problem 1344

What is the probability of picking a blue marble from an urn with 10 red, 29 blue, and 4 yellow marbles?

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Problem 1345

What is the probability that no women are chosen when selecting 2 members from 3 women and 2 men? Round to 4 decimal places.

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Problem 1346

What is the probability of selecting a red marble from an urn with 23 red, 31 blue, and 45 yellow marbles? Round to 4 decimal places.

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Problem 1347

Find the probability of drawing an ace or a black card from a 52-card deck. A) 713\frac{7}{13} B) 1526\frac{15}{26} C) 2952\frac{29}{52} D) 413\frac{4}{13}

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Problem 1348

What is the probability that a randomly selected Master's student majored in English or Mathematics? Round to three decimal places.

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Problem 1349

Survey 200 consumers about Crunchicles. Find probabilities for age groups and preferences. Answers in reduced fractions.
a. P(18-24 | dislikes) b. P(dislikes) c. P(35-55 or likes) d. P(likes | 70 years old)

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Problem 1350

Survey 300 consumers on Crunchicles. Find probabilities for age, preferences, and liking. Answers as reduced fractions.

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Problem 1351

Find the probability that a randomly chosen student is not female and did not earn grade C. Round to four decimal places.

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Problem 1352

Jamie spun a spinner 1000 times. Estimate the probability of landing on pink as a simplified fraction from his results.

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Problem 1353

What is the probability that Jonah picks an oatmeal cookie and then a sugar cookie from a bag of 6 chocolate chip, 5 peanut butter, 5 sugar, and 7 oatmeal cookies? Express as a reduced fraction.

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Problem 1354

A factory has 22 compressors with 5 defective. Find the probabilities for a sample of 5: all defective and none defective.

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Problem 1355

A standard deck has 52 cards: 26 black (clubs, spades) and 26 red (hearts, diamonds). Find the probability of:
1) Drawing a 7 of Clubs? 2) Drawing a Heart or Spade? 3) Drawing a number smaller than 3 (ace as 1)?

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Problem 1356

A jar has 5 red and 34 blue marbles. What is the probability of drawing 2 red marbles?

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Problem 1357

A die is rolled. Find the probabilities for these events: (a) showing a 2, (b) showing an even number, (c) greater than 2.

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Problem 1358

What is the probability of getting at most one heads when flipping two coins? Provide your answer as a reduced fraction.

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Problem 1359

A jar has 8 red and 12 blue marbles. Find probabilities for the following events (rounded to two decimal places): (a) Red marble (b) Odd-numbered marble (c) Red or odd-numbered marble

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Problem 1360

docs.google.com
Read carefully, then determine the correct answer. * \begin{tabular}{|l|c|c|c|} \hline & Under 30 & 30 or older & Total \\ \hline Male & 3 & & 12 \\ \hline Female & & & 20 \\ \hline Total & 8 & 24 & 32 \\ \hline \end{tabular}
The incomplete table above shows the distribution of age and gender for 32 people who entered a tennis tournament.
1
If a tennis player is chosen at random, what is the probability that the player will be either a male under age 30 or a female aged 30 or older? A) 1532\frac{15}{32} B) 1832\frac{18}{32} C) 2032\frac{20}{32} D) 2432\frac{24}{32}

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Problem 1361

Sales representatives at a car dealership were split into two groups. One group used an aggressive approach to sell a customer a new automobile. The other group used a passive approach. The following table summarizes the records for 657 customers. If one of these customers is selected at random, determine the probability that the passive approach was used. \begin{tabular}{|l|c|c|c|} \hline Approach & Sale & No Sale & Total \\ \hline Aggressive & 110 & 249 & 359 \\ Passive & 212 & 86 & 298 \\ \hline Total & 322 & 335 & 657 \\ \hline \end{tabular}
The probability that the passive approach was used is \square (Type an integer or a simplified fraction.)

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Problem 1362

In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student has a cat given that they have a dog?
Has a cat | Does not have a cat ------- | -------- Has a dog | 2 | 3 Does not have a dog | 7 | 18
Answer Attempt 1 out of 2

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Problem 1363

One coin is flipped and then one die is rolled.
What is the probability of getting a tail on the coin and a number less than 5 on the die?
Enter the number that belongs in the green box. Completely reduce the fraction before entering.

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Problem 1364

Question 3(Multiple Choice Worth 3 points) (Planning for Retirement LC)
An employee is 38 years old and has had a retirement account for 13 years, with about 29 years to go before retirement. Which breakdown of investments would a financial advisor most likely suggest for the employee at this point in time? 0\% high-risk, 10\% medium-risk, 90%90 \% low-risk 10%10 \% high-risk, 20%20 \% medium-risk, 70%70 \% low-risk 30%30 \% high-risk, 45%45 \% medium-risk, 25%25 \% low-risk 70%70 \% high-risk, 25%25 \% medium risk, 5%5 \% low-risk

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Problem 1365

Consider the probability distribution f(x)=(0.1904)(0.8096)x,x=0,1,2,3,4,5,f(x)=(0.1904)(0.8096)^{x}, x=0,1,2,3,4,5, \ldots Find P(X16)\mathrm{P}(X \geq 16). NOTE: give your answer to 6 decimal places. Example: "2.000000" (not simply "2").

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Problem 1366

Which pair of events are non-overlapping when rolling a single sixsided die? Getting a number greater than 5 Getting a number less than 3 Getting an odd number Getting a prime number Getting an even number Getting a number less than 3 Getting a number greater than 3 Getting a number less than 5

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Problem 1367

You select a family with three children. If MM represents a male child and FF a female child, the set of equally likely outcomes for the children's sexes is \{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}. Assuming that the probability of a male or female birth is 0.5 , find the probability of selecting a family with i) Exactly one female child? ii) Exactly two male children? i) 0.375 , ii) 0.125 i) 0.375 , ii) 0.375 i) 0.125 , ii) 0.375 i) 0.125 , ii) 0.125

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Problem 1368

SQQS1013 Pengantar Statistik No, Matrik: \qquad
SOALAN/ QUESTION 4 (25 MARKAH/MARKS) a) Satu kajian mendapati bahawa DUA (2) daripada TIGA (3) pelajar di Prince College mempunyai komputer riba. DUA (2) pelajar dipilih secara rawak dan katakan XX mewakili pembolehubah rawak bilangan pelajar yang tidak mempunyai komputer riba. Andaikan bahawa proses pemilihan adalah bebas. A survey found that TWO (2) out of THREE (3) students at Prince College own a laptop. TWO (2) students were randomly selected and let XX be the number of students who did NOT own a laptop. Assume that the selection processes are independent. i. Lukis gambarajah pokok untuk menggambarkan situasi di atas.
Draw a tree diagram to illustrate the situation above. (3 markah/marks) ii. Berdasarkan kepada jawapan di bahagian (a)(i), bina taburan kebarangkalian bagi XX. Based on the answer in part (a) (i), construct the probability distribution of XX. (4 markab/marks)

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Problem 1369

Swimming Pool Services A survey found that 5 in 10 private swimming pool owners employ a pool service to care for their swimming pools. Find each probability for a sample of 10 pool owners. Round intermediate calculations and final answers to three decimal places.
Part 1 of 3 (a) Fewer than 4 homeowners employ a pool service. P(P( fewer than 4 homeowners employ a pool service )=0.172)=0.172
Part: 1 / 3
Part 2 of 3 (b) Exactly 6 homeowners employ a pool service. PP (exactly 6 homeowners employ a pool service )=)= \square

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Problem 1370

If two dice are rolled one time, find Enter your answers as fractions or a:
Part: 0 / 4 \square
Part 1 of 4 (a) A sum of 4 P(P( sum of 4)=)= \square Skip Part Check Save For Later

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Problem 1371

18) For women aged 182418-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg . If 23 women aged 182418-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122 mm Hg . A) 0.9341 B) 0.0577 C) 0.3343 D) 0.0833 19) In a certain town, 22%22 \% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure. A) 4.6 voters 2{ }^{2} B) 13 voters 2^{2} C) 1.9 voters 2^{2} D) 3.6 voters 2^{2} 20) On a test, 74%74 \% of the questions are answered correctly. If 111 questions are correct, how many questions are on the test? A) 150 questions B) 37 questions (C) 82 questions D) 67 questions 21) The following table contains data from a study of two airlines which fly to Small Town, USA. If one flight is selected, find PP (on time and Upstate Airlines). 21) 20) \qquad 19) \qquad

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Problem 1372

Children's Obesity The following information shows the percentage of children who are obese for 3 age groups: \begin{tabular}{|c|c|} \hline Age & Percent \\ \hline 353-5 & 7.1 \\ \hline 6116-11 & 18.1 \\ \hline 121912-19 & 18.7 \\ \hline \end{tabular}
If a child is selected at random, find each probability.
Part: 0/20 / 2
Part 1 of 2 (a) If you select a 3-5 year old child, the child is obese.
The probability is \square \%.

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Problem 1373

What is the probability that both of two randomly selected people own dogs if 53%53\% of people have dogs? Provide as a decimal or fraction.

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Problem 1374

Find the probability that a randomly chosen student is male or received a grade of "B". Round to four decimal places.

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Problem 1375

A factory has 22 compressors, 5 of which are defective. Find the probabilities that all or none of a 5-compressor sample are defective as reduced fractions.

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Problem 1376

Find the probability of rolling an even number or a number less than 5 on a six-sided die.

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Problem 1377

What is the probability of drawing a diamond or a face card from a standard 52-card deck?

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Problem 1378

A basketball team leads at halftime 70%70\% of games, winning 75%75\% then, and 20%20\% otherwise. Find the overall win probability.

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Problem 1379

Find the probability that a randomly chosen student won an award for either English or math given 213 students, 78 in English, 61 in math, and 23 in both.

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Problem 1380

What is the probability of drawing a red card or a 7 from a standard deck of 52 cards? P(red7)P(\text{red} \cup 7)

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Problem 1381

What is the probability that neither you nor your friend wins if you have a 35%35\% chance to win and your friend has a 31%31\% chance?

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Problem 1382

A focus group of chips is 48%48\% female. If 35%35\% of females and 55%55\% of males would buy, find the overall probability.

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Problem 1383

The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $5\$ 5. There is 1 winning ticket out of the 230 tickets sold. The winner gets a prize worth $98\$ 98. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? \ \squareCalculatetheexpectedvalue(toyou)ifyoupurchase12raffletickets.$ Calculate the expected value (to you) if you purchase 12 raffle tickets. \$ \squareWhatistheexpectedvalue(tothePTO)ofoneraffleticket?$ What is the expected value (to the PTO) of one raffle ticket? \$ \squareIfthePTOsellsall230raffletickets,howmuchmoneycantheyexpecttoraisefortheclassroomsupplies?$ If the PTO sells all 230 raffle tickets, how much money can they expect to raise for the classroom supplies? \$ \square$

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Problem 1384

D) You pick a card at random.
1 2 3 4 5
What is P(\mathrm{P}( less than 4)) ? Write your answer as a percentage. \square \%

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Problem 1385

104. In an effort to find the source of an outbreak of food poisoning at a conference, a team of medical detectives carried out a study. They examined all 50 people who had food poisoning and a random sample of 200 people attending the conference who didn't get food poisoning. The detectives found that 40%40 \% of the people with food poisoning went to a cocktail party on the second night of the conference, while only 10%10 \% of the people in the random sample attended the same party. Which of the following statements is appropriate for describing the 40%40 \% of people who went to the party? (Let F=\mathrm{F}= got food poisoning and A=\mathrm{A}= attended party.) (a) P(FA)=0.40P(F \mid A)=0.40 (d) P( ACF)=0.40P\left(\mathrm{~A}^{\mathrm{C}} \mid \mathrm{F}\right)=0.40 (b) P(AFC)=0.40P\left(A \mid F^{C}\right)=0.40 (e) P(AF)=0.40P(A \mid F)=0.40 (c) P(FAC)=0.40P\left(F \mid A^{C}\right)=0.40

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Problem 1386

In a certain Algebra 2 class of 30 students, 14 of them play basketball and 7 of them play baseball. There are 14 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

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Problem 1387

```latex (e) Using a cutoff of 0.05, do you think it would be unusual for an individual to have an income of less than 33? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.
\square, because the probability that an individual has an income less than 33 is \square.
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 35. A pollster draws a sample of 91 people to interview. ```

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Problem 1388

The Gallup Poll reported that 56%56 \% of Americans want to lose weight. If 5 people are selected at random, find the probability that they all want to lose weight. Please round the final answer to 2 or 3 decimal places. P(5P(5 people wanted to lose weight )=)= \square

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Problem 1389

Probability Outcomes and event probability
A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of event. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline & \multicolumn{8}{|c|}{Outcomes} & \multirow{2}{*}{Probability} \\ \hline & EEO & OEO & 000 & EOO & OEE & EEE & EOE & OOE & \\ \hline Event A: An even number on the last roll & 0 & 0 & 0 & 0 & ○ & 0 & O & 0 & 38\frac{3}{8} \\ \hline Event B: An odd number on each of the first two rolls & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 14\frac{1}{4} \\ \hline Event C: An even number on both the first and the last rolls & 0 & 0 & 0 & 0 & 0 & 0 & 0 & ○ & \square \\ \hline \end{tabular}

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Problem 1390

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.07 . If 210 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.04 ? Round your answer to four decimal places.
Answer How to enter your answer (opens in new window) 2 Points Tables Keypad

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Problem 1391

2. Sonia has 5 yellow hair clips, 2 red hair clips, and 3 blue hair clips in her purse. What is the probe that she will randomly select one yellow hair clip and one blue hair clip without replacement? a) 1556\frac{15}{56} b) 320\frac{3}{20} 5+2+3=105+2+3=10 c) 16\frac{1}{6} d) 815\frac{8}{15} 4/92/8=4 / 9 * 2 / 8=

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Problem 1392

Question
The results of a survey of 39 students and the foreign language they are studying are shown in the twoway frequency table. \begin{tabular}{|c|c|c|c|c|} \cline { 2 - 5 } \multicolumn{1}{c|}{} & \multicolumn{4}{|c|}{ Language } \\ \hline Gender & Chinese & French & Spanish & Total \\ \hline GIrl & 3 & 7 & 10 & 20 \\ \hline Boy & 4 & 4 & 11 & 19 \\ \hline Total & 7 & 11 & 21 & 39 \\ \hline \end{tabular}
What fraction of the surveyed students are taking Chinese? \square of the surveyed students are taking Chinese.

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Problem 1393

12) O'Leary is starting a chess team and there are seven spots on the team. There are 8 Grade tens, 7 grade elevens, and 14 grade twleves that are trying to make the team. Assume each student is equally skilled and equally likely to make the team. a) How many different teams are possible? 29C7=1560780 possible teams { }_{29} C_{7}=1560780 \text { possible teams } b) What is the probability of the team consisting of 2 students from grade ten, 2 students from grade eleven, and 3 students from grade twelve? Express your answer as a percentage to the nearest te of a percent. 8C27C214C329C7=28213641560780=2140321560780=0.137×1\frac{8 C_{2} \cdot{ }_{7} C_{2} \cdot{ }_{14} C_{3}}{{ }_{29} C_{7}}=\frac{28 \cdot 21 \cdot 364}{1560780}=\frac{214032}{1560780}=0.137 \times 1 c) What is the probability of the team including either 1 or 2 students from grade ten? Express yo answer as a percentage to the nearest tenth of a percent.

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Problem 1394

A committee of 4 is being formed randomly from the employees at a school: 6 administrators, 38 teachers, and 5 staff. What is the probability that all 4 members are administrators? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts

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Problem 1395

The target in the figure shown to the right contains four squares. If a dart thrown at random hits the target, find the probability that it will land in a green region.
The probability that a dart will land in a green region of the square target is \square 0. (Type an integer or a simplified fraction.)

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Problem 1396

The target in the figure shown to the right contains four squares. If a dart thrown at random hits the target, find the probability that it will land in a green region.
The probability that a dart will land in a green region of the square target is \square (Type an integer or a simplified fraction.)

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Problem 1397

For the experiment of rolling a single fair die, find the probability that the number rolled is odd or even.
The probability that the number rolled is odd or even is \square . (Simplify your answer.)

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Problem 1398

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter.
If six neighbors with the same type of opener set their switches independently, what is the probability of at least one pair of neighbors using the same settings?
The probability of at least one pair of neighbors using the same settings is approximately 9785 . (Type an integer or decimal rounded to four decimal places as needed.)

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Problem 1399

The conditional probability of event B occurring, given that event A has occurred, is P(BA)=P(A and B)P(A).\text{The conditional probability of event } B \text{ occurring, given that event } A \text{ has occurred, is } P(B \mid A)=\frac{P(A \text{ and } B)}{P(A)}. Use the information below to find the probability that a flight departed on time given that it arrives on time.
The probability that an airplane flight departs on time is 0.89.\text{The probability that an airplane flight departs on time is } 0.89.
The probability that a flight arrives on time is 0.87.\text{The probability that a flight arrives on time is } 0.87.
The probability that a flight both departs and arrives on time is 0.82.\text{The probability that a flight both departs and arrives on time is } 0.82.

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Problem 1400

A clown made purple and green balloon animals. What is the probability a randomly selected one is green and a dog? Simplify.

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