Question

A college student is taking two courses. The probability she passes the first course is 0.67. The probability she passes the second course is 0.7. The probability she passes at least one of the courses is 0.79. Give your answer to four decimal places. a. What is the probability she passes both courses

Answer 1

0.58 = 58% probability she passes both courses

Explanation:

We can solve this question treating the probabilities as a Venn set.

I am going to say that:

Event A: She passes the first course.

Event B: She passes the second course.

The probability she passes the first course is 0.67.

This means that
`P(A) = 0.67`

The probability she passes the second course is 0.7.

This means that
`P(B) = 0.7`

The probability she passes at least one of the courses is 0.79.

This means that
`P(A \cup B) = 0.79`

a. What is the probability she passes both courses

This is
`P(A \cap B)`.

We use the following relation:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

So

`P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.67 + 0.7 - 0.79 = 0.58`

0.58 = 58% probability she passes both courses