Enrichment: Conditional Probability

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 Textbook (Glencoe Algebra 1 - ISBN: 9780028253282) into html format.

Enrichment
Conditional Probability

The probability of an event given the occurence of another event is called Conditional Probability. The conditional probability of event A given event B is denoted P(A|B).

Example:

Suppose a pair of number cubes is rolled. It is known that the sum is greater than seven. Find the probability that the number cubes match.

There are 15 sums greater than seven and there are 36 possible pairs altogether.

P(B) =

P(A|B) =

P(A and B)

P(B)

3/36

15/36

The conditional probability is 1/5.

There are three matching pairs greater than seven: (4,4) (5,5) (6,6)

P(A and B) =

A card is drawn from a standard deck of 52 cards and is found to be red. Given that event, find each of the following probabilities.

1. P(heart)

1/2

2. P(ace)

1/13

3. P(face card)

3/13

4. P(jack or ten)

2/13

5. P(six of spades)

3. P(six of hearts)

1/26

A sports survey taken at Stirers High School shows that 48% of the respondents liked soccer, 66% liked basketball, and 38% likes hockey. Also 30% liked soccer and backetball, 22% liked basketball and hockey, and 28% liked soccer and hockey. Finally, 12% liked all three sports.

7. Find the probability that Meg likes soccer if she likes basketball.

5/11

8. Find the probability that Juan likes Basketball if he likes soccer.

5/8

9. Find the probability that Mieko likes hockey if she likes basketball.

1/3

10. Find the probability that Greg likes hockey if he likes soccer.

7/12