Question

A college student is taking two courses. The probability she passes the first course is 0.7. The probability she passes the second course is 0.67. 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 have two events, A and B.

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

In which:

`P(A \cup B)` is the probability of at least one of these events happening.

P(A) is the probability of A happening.

P(B) is the probability of B happening.

`P(A \cap B)` is the probability of both happening.

In this question:

Event A: Passes the first course.

Event B: Passes the second course.

The probability she passes the first course is 0.7.

This means that
`P(A) = 0.7`

The probability she passes the second course is 0.67.

This means that
`P(B) = 0.67`

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

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

What is the probability she passes both courses

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

`0.79 = 0.70 + 0.67 - P(A \cap B)`

`P(A \cap B) = 0.58`

0.58 = 58% probability she passes both courses