Question

Thirty percent of students in a calculus class and twenty percent of students in a statistics course receive A’s. Furthermore, 60 percent of students with an A in calculus receive an A in the statistics course. What is the probability that a student who receives an A in statistics will also receive an A in calculus?

Answer 1

90% probability that a student who receives an A in statistics will also receive an A in calculus

Explanation:

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

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

P(A) is the probability of A happening.

In this question:

Event A: A in statistics.

Event B: A is calculus

Twenty percent of students in a statistics course receive A’s.

This means that
`P(A) = 0.2`

Furthermore, 60 percent of students with an A in calculus receive an A in the statistics course.

Thirty percent of students in a calculus class receive an A.

This means that
`P(A \cap B) = 0.6*0.3 = 0.18`

What is the probability that a student who receives an A in statistics will also receive an A in calculus?

`P(B|A) = (0.18)/(0.2) = 0.9`

90% probability that a student who receives an A in statistics will also receive an A in calculus