Question

[4] Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 65% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 10% 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.

Answer 1

Let R shows the event that student goes to the statistics laboratory on a regular basis. Let A shows the event that student get grade A.

From the given information we have

P(R) = 0.40, P(A|R) = 0.65, P(A|R') = 0.10

By the complement rule,

P(R') = 1 - P(R) = 0.60

By the Bayes theorem, the probability that she or he used the lab on a regular basis given that particular student made an A is

P(R | A) = [ P(A|R)P(R) ] / [ P(A|R)P(R) + P(A|R')P(R') ] = [ 0.65 * 0.40 ] / [ 0.65 * 0.40 + 0.10 * 0.60 ] = 0.8125

Answer: 0.8125