13.7 Probability  (Page 6/18)

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Landing on a vowel

$\text{\hspace{0.17em}}\frac{1}{2}.\text{\hspace{0.17em}}$

Not landing on blue

Landing on purple or a vowel

$\text{\hspace{0.17em}}\frac{5}{8}.\text{\hspace{0.17em}}$

Landing on blue or a vowel

Landing on green or blue

$\text{\hspace{0.17em}}\frac{1}{2}.\text{\hspace{0.17em}}$

Landing on yellow or a consonant

Not landing on yellow or a consonant

$\text{\hspace{0.17em}}\frac{3}{8}.\text{\hspace{0.17em}}$

For the following exercises, two coins are tossed.

What is the sample space?

Find the probability of tossing two heads.

$\text{\hspace{0.17em}}\frac{1}{4}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly one tail.

Find the probability of tossing at least one tail.

$\text{\hspace{0.17em}}\frac{3}{4}.\text{\hspace{0.17em}}$

For the following exercises, four coins are tossed.

What is the sample space?

Find the probability of tossing exactly two heads.

$\text{\hspace{0.17em}}\frac{3}{8}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly three heads.

Find the probability of tossing four heads or four tails.

$\text{\hspace{0.17em}}\frac{1}{8}.\text{\hspace{0.17em}}$

Find the probability of tossing all tails.

Find the probability of tossing not all tails.

$\text{\hspace{0.17em}}\frac{15}{16}.\text{\hspace{0.17em}}$

Find the probability of tossing exactly two heads or at least two tails.

$\text{\hspace{0.17em}}\frac{5}{8}.\text{\hspace{0.17em}}$

For the following exercises, one card is drawn from a standard deck of $\text{\hspace{0.17em}}52\text{\hspace{0.17em}}$ cards. Find the probability of drawing the following:

A club

A two

$\text{\hspace{0.17em}}\frac{1}{13}.\text{\hspace{0.17em}}$

Six or seven

Red six

$\text{\hspace{0.17em}}\frac{1}{26}.\text{\hspace{0.17em}}$

An ace or a diamond

A non-ace

$\text{\hspace{0.17em}}\frac{12}{13}.\text{\hspace{0.17em}}$

A heart or a non-jack

For the following exercises, two dice are rolled, and the results are summed.

Construct a table showing the sample space of outcomes and sums.

1 2 3 4 5 6
1 (1, 1)
2
(1, 2)
3
(1, 3)
4
(1, 4)
5
(1, 5)
6
(1, 6)
7
2 (2, 1)
3
(2, 2)
4
(2, 3)
5
(2, 4)
6
(2, 5)
7
(2, 6)
8
3 (3, 1)
4
(3, 2)
5
(3, 3)
6
(3, 4)
7
(3, 5)
8
(3, 6)
9
4 (4, 1)
5
(4, 2)
6
(4, 3)
7
(4, 4)
8
(4, 5)
9
(4, 6)
10
5 (5, 1)
6
(5, 2)
7
(5, 3)
8
(5, 4)
9
(5, 5)
10
(5, 6)
11
6 (6, 1)
7
(6, 2)
8
(6, 3)
9
(6, 4)
10
(6, 5)
11
(6, 6)
12

Find the probability of rolling a sum of $\text{\hspace{0.17em}}3.\text{\hspace{0.17em}}$

Find the probability of rolling at least one four or a sum of $\text{\hspace{0.17em}}8.$

$\text{\hspace{0.17em}}\frac{5}{12}.$

Find the probability of rolling an odd sum less than $\text{\hspace{0.17em}}9.$

Find the probability of rolling a sum greater than or equal to $\text{\hspace{0.17em}}15.$

$\text{\hspace{0.17em}}0.$

Find the probability of rolling a sum less than $\text{\hspace{0.17em}}15.$

Find the probability of rolling a sum less than $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ or greater than $\text{\hspace{0.17em}}9.$

$\text{\hspace{0.17em}}\frac{4}{9}.\text{\hspace{0.17em}}$

Find the probability of rolling a sum between $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}9\text{,}\text{\hspace{0.17em}}$ inclusive.

Find the probability of rolling a sum of $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}6.\text{\hspace{0.17em}}$

$\text{\hspace{0.17em}}\frac{1}{4}.\text{\hspace{0.17em}}$

Find the probability of rolling any sum other than $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}6.\text{\hspace{0.17em}}$

For the following exercises, a coin is tossed, and a card is pulled from a standard deck. Find the probability of the following:

A head on the coin or a club

$\text{\hspace{0.17em}}\frac{3}{4}\text{\hspace{0.17em}}$

A tail on the coin or red ace

A head on the coin or a face card

$\text{\hspace{0.17em}}\frac{21}{26}\text{\hspace{0.17em}}$

No aces

For the following exercises, use this scenario: a bag of M&Ms contains $\text{\hspace{0.17em}}12\text{\hspace{0.17em}}$ blue, $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ brown, $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ orange, $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ yellow, $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ red, and $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ green M&Ms. Reaching into the bag, a person grabs 5 M&Ms.

What is the probability of getting all blue M&Ms?

$\text{\hspace{0.17em}}\frac{C\left(12,5\right)}{C\left(48,5\right)}=\frac{1}{2162}\text{\hspace{0.17em}}$

What is the probability of getting $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ blue M&Ms?

What is the probability of getting $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ blue M&Ms?

$\frac{C\left(12,3\right)C\left(36,2\right)}{C\left(48,5\right)}=\frac{175}{2162}$

What is the probability of getting no brown M&Ms?

Extensions

Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ numbers from the numbers $\text{\hspace{0.17em}}1\text{\hspace{0.17em}}$ to $\text{\hspace{0.17em}}80.\text{\hspace{0.17em}}$ After the player makes his selections, $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ winning numbers are randomly selected from numbers $\text{\hspace{0.17em}}1\text{\hspace{0.17em}}$ to $\text{\hspace{0.17em}}80.\text{\hspace{0.17em}}$ A win occurs if the player has correctly selected $\text{\hspace{0.17em}}3,4,\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ of the $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ winning numbers. (Round all answers to the nearest hundredth of a percent.)

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