Question

18% of all students at West Colon High School play baseball and 32% play soccer. The probability that a student plays baseball given that the student plays soccer is 22%. Calculate the probability that a student plays both baseball and soccer.

a. 0.6875
b. 02275
c. 0.0396
d. 1.2222
e. 0.0704
f. 0.0576

Answer 1

e. 0.0704

Explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a student plays baseball.

B is the probability that a student plays soccer.

We have that:

`A = a + (A \cap B)`

In which a is the probability that a student plays baseball but not soccer and
`A \cap B` is the probability that a student plays both of these sports.

By the same logic, we have that:

`B = b + (A \cap B)`

18% of all students at West Colon High School play baseball and 32% play soccer.

This means that
`A = 0.18, B = 0.32`

The probability that a student plays baseball given that the student plays soccer is 22%.

This means that

`(A \cap B)/(B) = 0.22`

Calculate the probability that a student plays both baseball and soccer.

This is
`A \cap B`

`(A \cap B)/(B) = 0.22`

`(A \cap B)/(0.32) = 0.22`

`A \cap B = 0.32*0.22 = 0.0704`

So the correct answer is:

e. 0.0704