• conditional probability

• contingency table

• relative frequency

Conditional Probability

Kim draws a card from a standard 52-card deck. What is the probability that she draws a heart given that the card is from a red suit?

There are 26 red cards in a deck. There are 13 hearts.

Let event A be that she drew a red card.

Let event B be that she drew a heart.

26 of the 52 cards are of a red suit.

13 of the 52 cards are of a red suit and a heart

Conditional Probability

Probability of B given A

Answer: The probability of drawing a card that was

a heart given that the card is from a red suit

is .

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Vitali draws a card from a standard 52-card deck. What is the probability that she draws a Jack given that the card she drew is a face card?

A.

B.

C.

D.

Contingency Tables

COLLEGE Find the probability that a student plans to attend college after high school if the student is a girl.

Contingency Tables

There is a total of 342 + 376 + 151 + 138 or 907 people in the study. We need to find the probability of girls planning to attend college after high school.

Conditional Probability Formula

Contingency Tables

Answer: The probability that a student plans to attend college after high school if the student is a girl is about 0.73 or 73%.

Simplify.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 13.7%

B. 30.6%

C. 34.0%

D. 37.3%

COLLEGE Find the probability that a student does not plan to attend college after high school if the student is a boy.

The table shows the number of students who are varsity athletes. Find the probability that a student is non-varsity given that he or she is a senior.

A 16.6%

B 19.8%

C 50.4%

D 83.4%

Read the Test Item

We need to find the probability that a student is non-varsity given that he or she is a senior. There is a total of 1180 students.

Solve the Test Item

Conditional Probability Formula

Simplify.

Answer: The probability is about 83.4%. The correct answer is D.

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

A. 6.5%

B. 7.1%

C. 7.7%

D. 8.4%

The table shows the number of students who are varsity athletes. Find the probability that a student is varsity given that he or she is a sophomore.