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 …

Question

asked Dec 26, 2021 16.2k views

1 Answer

Wayner · Answer 1 · 2022-01-01T03:18:52+0000

Answer:

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