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

Answer:

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

Step-by-step explanation:

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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?

$P(B|A) = \frac{0.18}{0.2} = 0.9$

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