Math / Data & Statistics

Question14 123 Defaul... B A B5:B8 fx 100\% \ $\% .0$ \xrightarrow{00}I5 \frac{2}{2}$ 17 B A Answer Note: your answers ca decimals or percentage Question
You roll a fair, 5 -sided die. What's the probability you will roll a 3? A bag contains a bunch of marbles: 13 red, 10 green, and 4 yellow. What's the probability of randomly picking a green marble? A bag contains a bunch of marbles: 13 red, 10 green, and 4 yellow. What's the probability of randomly picking a yellow marble? A bag contains a bunch of marbles: 13 red, 10 green, and 4 yellow. What's the probability of randomly picking a red OR green marble? Imagine a spinner with every number (in order) from 1 to $\mathbf{2 0}$ . What are the chances it will land on a multiple of 3 ? (that means 3 or 6 or 9 or 12 or 15 or 18) Imagine a spinner with every number (in order) from 1 to 20 . What are the chances it will land exactly on the number I'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{2 0}$ . What are the chances it will land within one tile (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to 10. What are the chances it will land within two tiles (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{3 0}$ . What are the chances it will land within three tiles (on Level1 - Level 2 . Level 3 -

Studdy Solution

STEP 1

What is this asking? What are the chances of different events happening, like rolling a certain number on a die or picking a specific color marble from a bag? Watch out! Don't forget to count all the possibilities correctly!
Make sure you're looking at the total number of outcomes when calculating probabilities.

STEP 2

1. Die Roll
2. Green Marble
3. Yellow Marble
4. Red or Green Marble
5. Multiple of 3
6. Specific Number (1-20)
7. Within One Tile (1-20)
8. Within Two Tiles (1-10)

STEP 3

We're looking for the probability of rolling a 3 on a 5-sided die.
Since the die is fair, each side has an equal chance of showing up.

STEP 4

There's only one favorable outcome (rolling a 3) out of a total of $5$ possible outcomes (1, 2, 3, 4, 5).

STEP 5

So, the probability is $\frac{\textbf{Favorable Outcomes}}{\textbf{Total Outcomes}} = \frac{1}{5}$ .

STEP 6

We have a bag with 13 red, 10 green, and 4 yellow marbles.
We want to find the probability of picking a green marble.

STEP 7

The total number of marbles is $13 + 10 + 4 = 27$ .
There are 10 green marbles.

STEP 8

The probability of picking a green marble is $\frac{\textbf{Number of Green Marbles}}{\textbf{Total Number of Marbles}} = \frac{10}{27}$ .

STEP 9

Using the same marble counts as before, we want the probability of picking a yellow marble.

STEP 10

There are 4 yellow marbles out of a total of $27$ marbles.

STEP 11

The probability is $\frac{4}{27}$ .

STEP 12

Now we want the probability of picking a red or a green marble.

STEP 13

There are 13 red marbles and 10 green marbles.
That's $13 + 10 = 23$ red or green marbles.

STEP 14

The probability is $\frac{\textbf{Red or Green Marbles}}{\textbf{Total Marbles}} = \frac{23}{27}$ .

STEP 15

We have a spinner with numbers from 1 to 20.
We want the probability of landing on a multiple of 3.

STEP 16

The multiples of 3 are 3, 6, 9, 12, 15, and 18.
That's 6 numbers.

STEP 17

The probability is $\frac{6}{20} = \frac{3}{10}$ .

STEP 18

What's the probability of the spinner landing on a specific number between 1 and 20?

STEP 19

There's only one specific number out of 20 possible numbers.

STEP 20

The probability is $\frac{1}{20}$ .

STEP 21

We want the probability of landing within one tile (on either side) of a specific number on the 1-20 spinner.

STEP 22

That means we could land on the number itself, the number before it, or the number after it.
That's 3 possible numbers (unless the specific number is 1 or 20, in which case there are only 2 possibilities, or if the number is 1 or 20, in which case there is only 1 possibility.
Let's assume the teacher is thinking of a number between 2 and 19 inclusive).

STEP 23

The probability is $\frac{3}{20}$ .

STEP 24

Now we have a spinner from 1 to 10, and we want the probability of landing within two tiles of a specific number.

STEP 25

That's the number itself, two numbers before it, and two numbers after it.
That's a potential of 5 numbers.
Again, we'll assume the number is between 3 and 8 inclusive.

STEP 26

The probability is $\frac{5}{10} = \frac{1}{2}$ .

STEP 27

The probabilities are: rolling a 3 (1/5), picking a green marble (10/27), picking a yellow marble (4/27), picking a red or green marble (23/27), landing on a multiple of 3 (3/10), landing on a specific number (1/20), landing within one tile (3/20), and landing within two tiles (1/2).

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Die Roll2. Green Marble3. Yellow Marble4. Red or Green Marble5. Multiple of 36. Specific Number (1-20)7. Within One Tile (1-20)8. Within Two Tiles (1-10)

STEP 3

We're looking for the probability of rolling a **3** on a **5**-sided die.Since the die is fair, each side has an equal chance of showing up.

STEP 4

There's only **one** favorable outcome (rolling a 3) out of a **total** of 555 possible outcomes (1, 2, 3, 4, 5).

STEP 5

So, the probability is Favorable OutcomesTotal Outcomes=15\frac{\textbf{Favorable Outcomes}}{\textbf{Total Outcomes}} = \frac{1}{5}Total OutcomesFavorable Outcomes​=51​.

STEP 6

We have a bag with **13 red**, **10 green**, and **4 yellow** marbles.We want to find the probability of picking a green marble.

STEP 7

The **total** number of marbles is 13+10+4=2713 + 10 + 4 = 2713+10+4=27.There are **10** green marbles.

STEP 8

The probability of picking a green marble is Number of Green MarblesTotal Number of Marbles=1027\frac{\textbf{Number of Green Marbles}}{\textbf{Total Number of Marbles}} = \frac{10}{27}Total Number of MarblesNumber of Green Marbles​=2710​.

STEP 9

Using the same marble counts as before, we want the probability of picking a yellow marble.

STEP 10

There are **4** yellow marbles out of a **total** of 272727 marbles.

STEP 11

The probability is 427\frac{4}{27}274​.

STEP 12

Now we want the probability of picking a red *or* a green marble.

STEP 13

There are **13 red** marbles and **10 green** marbles.That's 13+10=2313 + 10 = 2313+10=23 red or green marbles.

STEP 14

The probability is Red or Green MarblesTotal Marbles=2327\frac{\textbf{Red or Green Marbles}}{\textbf{Total Marbles}} = \frac{23}{27}Total MarblesRed or Green Marbles​=2723​.

STEP 15

We have a spinner with numbers from 1 to 20.We want the probability of landing on a multiple of 3.

STEP 16

The multiples of 3 are 3, 6, 9, 12, 15, and 18.That's **6** numbers.

STEP 17

The probability is 620=310\frac{6}{20} = \frac{3}{10}206​=103​.

STEP 18

What's the probability of the spinner landing on a specific number between 1 and 20?

STEP 19

There's only **one** specific number out of **20** possible numbers.

STEP 20

The probability is 120\frac{1}{20}201​.

STEP 21

We want the probability of landing within one tile (on either side) of a specific number on the 1-20 spinner.

STEP 22

STEP 23

The probability is 320\frac{3}{20}203​.

STEP 24

Now we have a spinner from 1 to 10, and we want the probability of landing within two tiles of a specific number.

STEP 25

That's the number itself, two numbers before it, and two numbers after it.That's a potential of **5** numbers.Again, we'll assume the number is between 3 and 8 inclusive.

STEP 26

The probability is 510=12\frac{5}{10} = \frac{1}{2}105​=21​.

STEP 27

The probabilities are: rolling a 3 (1/5), picking a green marble (10/27), picking a yellow marble (4/27), picking a red or green marble (23/27), landing on a multiple of 3 (3/10), landing on a specific number (1/20), landing within one tile (3/20), and landing within two tiles (1/2).

Get Studdy

Studdy solves anything!

Start learning now

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

1. Die Roll
2. Green Marble
3. Yellow Marble
4. Red or Green Marble
5. Multiple of 3
6. Specific Number (1-20)
7. Within One Tile (1-20)
8. Within Two Tiles (1-10)

We're looking for the probability of rolling a 3 on a 5-sided die.
Since the die is fair, each side has an equal chance of showing up.

There's only one favorable outcome (rolling a 3) out of a total of $5$ possible outcomes (1, 2, 3, 4, 5).

So, the probability is $\frac{\textbf{Favorable Outcomes}}{\textbf{Total Outcomes}} = \frac{1}{5}$ .

We have a bag with 13 red, 10 green, and 4 yellow marbles.
We want to find the probability of picking a green marble.

The total number of marbles is $13 + 10 + 4 = 27$ .
There are 10 green marbles.

The probability of picking a green marble is $\frac{\textbf{Number of Green Marbles}}{\textbf{Total Number of Marbles}} = \frac{10}{27}$ .

There are 4 yellow marbles out of a total of $27$ marbles.

The probability is $\frac{4}{27}$ .

Now we want the probability of picking a red or a green marble.

There are 13 red marbles and 10 green marbles.
That's $13 + 10 = 23$ red or green marbles.

The probability is $\frac{\textbf{Red or Green Marbles}}{\textbf{Total Marbles}} = \frac{23}{27}$ .

We have a spinner with numbers from 1 to 20.
We want the probability of landing on a multiple of 3.

The multiples of 3 are 3, 6, 9, 12, 15, and 18.
That's 6 numbers.

The probability is $\frac{6}{20} = \frac{3}{10}$ .

There's only one specific number out of 20 possible numbers.

The probability is $\frac{1}{20}$ .

The probability is $\frac{3}{20}$ .

That's the number itself, two numbers before it, and two numbers after it.
That's a potential of 5 numbers.
Again, we'll assume the number is between 3 and 8 inclusive.

The probability is $\frac{5}{10} = \frac{1}{2}$ .