Question

A teacher has found that the probability that a student studies for a test is 0.68, and the probability that a student gets a good grade on a test is 0.67, and the probability that both occur is 0.48.

A. Given that a student studies, find the probability that the student gets a good grade.

A) 0.68
B) 0.67
C) 0.48
D) 0.90

Answer 1

To find the probability that a student gets a good grade given that they have studied, we can use the conditional probability formula.

Step-by-step explanation:

To find the probability that a student gets a good grade given that they have studied, we can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case:

• A is the event that the student gets a good grade
• B is the event that the student studies
• P(A and B) is given as 0.48
• P(B) is given as 0.68

Substituting the values into the formula:

P(A|B) = 0.48 / 0.68 = 0.7059

Therefore, the probability that a student gets a good grade given that they have studied is approximately 0.71, which is closest to option B) 0.67.