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

Answer:

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

Step-by-step explanation:

Conditional Probability

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: 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.

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.22}{0.31} = 0.71$

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