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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.
Find the probability of tossing either two heads or three heads.
$\text{\hspace{0.17em}}\frac{5}{8}.\text{\hspace{0.17em}}$
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 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
$\text{\hspace{0.17em}}\frac{21}{26}\text{\hspace{0.17em}}$
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?
$\text{\hspace{0.17em}}\frac{C(12,5)}{C(48,5)}=\frac{1}{2162}\text{\hspace{0.17em}}$
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?
$\frac{C(12,3)C(36,2)}{C(48,5)}=\frac{175}{2162}$
What is the probability of getting no brown M&Ms?
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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