• probability

• success

• failure

• sample space

• random variable

• probability distribution

Probability with Combinations

Roman has a collection of 26 books—16 are fiction and 10 are nonfiction. He randomly chooses 8 books to take with him on vacation. What is the probability that he chooses 4 fiction and 4 nonfiction?

Step 1 Determine how many 8-book selections meet the conditions.

16C4 4 fiction books chosen from 16fiction books

10C4 4 nonfiction books chosen from10 nonfiction books

Probability with Combinations

Step 2 Find the total number, s + f, of possible 8-book selections.

Step 3 Determine the probability.

P(4 fiction, 4 nonfiction)

Use the Fundamental Counting Principle to find s, the number of successes.

Probability with Combinations

Use a calculator.

Answer: The probability is about 0.24464 or 24.5%.

Substitute.

Probability formula

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 0.7%

B. 18.1%

C. 39.2%

D. 46.7%

Ensley has a collection of 15 CDs—5 are jazz and 10 are blues. She randomly chooses 7 CDs to take with her on vacation. What is the probability that she chooses 2 jazz and 5 blues?

Probability with Permutations

For next semester, Alisa has signed up for English, precalculus, Spanish, geography, and chemistry classes. If classes are assigned randomly and each class is equally likely to be at any time of day, what is the probability that Alisa's first two classes in the morning will be precalculus and chemistry, in either order.

Step 1 Determine how many class arrangements meet the conditions.

2P2 Choose the first 2 classes.

3P3 Choose the other 3 classes.

Probability with Permutations

2P2 ● 3P3 = 2! ● 3! or 12

Step 2 Find the total number, s + f, of possible 5-class selections.

5P5 = 5! or 120 s + f = 120

Use the Fundamental Counting Principle to find the number of successes.

Step 3 Determine the probability.

P(precalculus, chemistry, followed by other classes)

Probability with Permutations

Answer: The probability of Alisa scheduling precalculus and chemistry as her first two classes is 0.1 or 10%.

Probability formula

Substitute.

Use a calculator.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6.7%

B. 7.4%

C. 8.3%

D. 8.5%

Travis and Cody are competing against four other athletes in the javelin throw. If all of the athletes randomly draw for the order in which they will throw, what is the probability that Travis and Cody will throw first or second in any order?

Probability with Combinations and

Permutations

Suppose Alice draws 4 cards without replacement from a standard 52-card deck. What is the probability that those 4 cards contain 2 of one suit and 2 of another?

Step 1 Determine the number of successes.

4P2 2 suits chosen from 4 if order matters

13C2 2 cards of one color chosen from a group of 13

13C2 2 cards of one color chosen from a group of 13

Probability with Combinations and

Permutations

Use permutations and combinations, along with the Fundamental Counting Principle, to find s.

4P2 ● 13C2 ● 13C2 = 12 ● 78 ● 78 or 73,008

Step 2 Determine the number of possibilities, s + f.

52C4 = 270,725 ways to choose 4 cards froma deck of 52.

Probability with Combinations and

Permutations

Step 3 Find the probability.

Probability of success

s = 73,008 and s + f = 270,725

≈ 0.2697 Use a calculator.

Answer: The probability that Alice draws 4 cards that contain 2 of one suit and 2 of another is about 0.2697 or 27%.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 4.8%

B. 5.6%

C. 6.1%

D. 6.8%

Suppose Alice draws 6 cards without replacement from a standard 52-card deck. What is the probability that those 6 cards contain 3 of one suit and 3 of another?

Probability Distribution

A. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. Create a relative-frequency graph of the probability distribution.

Answer:

Probability Distribution

B. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. Use the graph to determine which outcome is most likely. What is its probability?

Answer: The most likely outcome is green, and its

probability is .

Probability Distribution

C. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. What is the probability of drawing a red or blue marble?

Answer: The probability of drawing a red or blue

marble is .

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. Create a relative-frequency graph of the probability distribution.

A. B.

C. D.

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

B. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. Use the graph to determine which outcome is most likely. What is its probability?

A. grey;

B. purple;

C. grey;

D. clear;

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

C. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. What is the probability of drawing a grey or clear marble?

A.

B.

C.

D.