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

Answer:

e. 0.0704

Step-by-step 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

$\frac{A \cap B}{B} = 0.22$

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

This is $A \cap B$

$\frac{A \cap B}{B} = 0.22$

$\frac{A \cap B}{0.32} = 0.22$

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

So the correct answer is:

e. 0.0704