# 11.7 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.)

how fast can i understand functions without much difficulty
what is set?
a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
I got 300 minutes. is it right?
Patience
no. should be about 150 minutes.
Jason
It should be 158.5 minutes.
Mr
ok, thanks
Patience
100•3=300 300=50•2^x 6=2^x x=log_2(6) =2.5849625 so, 300=50•2^2.5849625 and, so, the # of bacteria will double every (100•2.5849625) = 258.49625 minutes
Thomas
what is the importance knowing the graph of circular functions?
can get some help basic precalculus
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
can get some help inverse function
ismail
Rectangle coordinate
how to find for x
it depends on the equation
Robert
yeah, it does. why do we attempt to gain all of them one side or the other?
Melissa
whats a domain
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
Spiro; thanks for putting it out there like that, 😁
Melissa
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
difference between calculus and pre calculus?
give me an example of a problem so that I can practice answering
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
I want to learn about the law of exponent
explain this