Math  /  Data & Statistics

Question15 Fill in the Blank 1 point
Determine if the scenario involves independent or dependent events. Then find the probability. You select a card from a standard shuffled deck of 52 cards. You return the card, shuffle, and then select another card. Both times the card is a diamond. (Note that 13 of the 52 cards are diamonds.) Type of probability: \square Probability (as a fraction) : type your answer... \square 16 Fill in the Blank 1 point
Determine if the scenario involves independent or dependent events. Then find the probability. You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows an even number. Type of probability: \square Probability (as a fraction) : type your answer... \square 17 Fill in the Blank 1 point
Determine if the scenario involves independent or dependent events. Then find the probability. There are fifteen shirts in your closet, seven blue and eight green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear green shirts both days. Type of probability: choose your answer... \square Probability (as a fraction): type your answer...

Studdy Solution

STEP 1

What is this asking? We've got three probability puzzles to crack: picking diamonds from a deck of cards (with replacement!), getting heads and an even number, and grabbing green shirts from a closet (without replacement, sneaky!). Watch out! Don't mix up independent and dependent events!
Returning the card to the deck makes a BIG difference.
Also, make sure to simplify those fractions!

STEP 2

1. Diamonds from a Deck
2. Coin Flip and Die Roll
3. Green Shirts Surprise

STEP 3

**Determine if the events are independent or dependent.** Since we put the first card back and shuffle, the second pick isn't affected by the first.
These are **independent** events!

STEP 4

**Calculate the probability of picking a diamond.** There are **13** diamonds out of **52** cards, so the probability is 1352=14\frac{13}{52} = \frac{1}{4}.

STEP 5

**Calculate the probability of picking two diamonds.** Since the events are independent, we **multiply** the individual probabilities: 1414=116\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}.

STEP 6

**Determine if the events are independent or dependent.** Flipping a coin doesn't affect rolling a die, so these are **independent** events!

STEP 7

**Calculate the probability of heads.** There's **1** head out of **2** sides, so the probability is 12\frac{1}{2}.

STEP 8

**Calculate the probability of an even number on a die.** There are **3** even numbers (2, 4, 6) out of **6** possible outcomes, so the probability is 36=12\frac{3}{6} = \frac{1}{2}.

STEP 9

**Calculate the probability of both events happening.** Since they're independent, we **multiply**: 1212=14\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}.

STEP 10

**Determine if the events are independent or dependent.** Since we're not putting the first shirt back, the second pick is affected by the first.
These are **dependent** events!

STEP 11

**Calculate the probability of picking a green shirt on Monday.** There are **8** green shirts out of **15** total, so the probability is 815\frac{8}{15}.

STEP 12

**Calculate the probability of picking a green shirt on Tuesday.** Now there are only **7** green shirts left and **14** total shirts, so the probability is 714=12\frac{7}{14} = \frac{1}{2}.

STEP 13

**Calculate the probability of both events happening.** Since they're dependent, we **multiply**: 81512=830=415\frac{8}{15} \cdot \frac{1}{2} = \frac{8}{30} = \frac{4}{15}.

STEP 14

1. **Type of probability:** Independent **Probability:** 116\frac{1}{16}
2. **Type of probability:** Independent **Probability:** 14\frac{1}{4}
3. **Type of probability:** Dependent **Probability:** 415\frac{4}{15}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord