Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We have two events, A and B.
![P(A \cup B) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%20%5Ccap%20B%29)
In which:
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.
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](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.7)
The probability she passes the second course is 0.67.
This means that ![P(B) = 0.67](https://tex.z-dn.net/?f=P%28B%29%20%3D%200.67)
The probability she passes at least one of the courses is 0.79.
This means that ![P(A \cup B) = 0.79](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%20%3D%200.79)
What is the probability she passes both courses
![P(A \cup B) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%20%5Ccap%20B%29)
![0.79 = 0.70 + 0.67 - P(A \cap B)](https://tex.z-dn.net/?f=0.79%20%3D%200.70%20%2B%200.67%20-%20P%28A%20%5Ccap%20B%29)
![P(A \cap B) = 0.58](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.58)
0.58 = 58% probability she passes both courses