Question

Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 55% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 15% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. (Round your answer to three decimal places.)

Answer 1

0.71 = 71% probability that she or he used the lab on a regular basis.

Explanation:

Conditional Probability

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: Student got an A

Event B: Used the lab on a regular basis.

Probability of an student getting an A:

55% of 40%(go to the lab on a regular basis).

15% of 100 - 40 = 60%(do not go to the lab on a regular basis).

So

`P(A) = 0.55*0.4 + 0.15*0.6 = 0.31`

Probability of getting an A and using the lab on a regular basis:

55% of 40%, so:

`P(A \cap B) = 0.55*0.4 = 0.22`

Probability that she or he used the lab on a regular basis.

`P(B|A) = (P(A \cap B))/(P(A)) = (0.22)/(0.31) = 0.71`

0.71 = 71% probability that she or he used the lab on a regular basis.