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 70% 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. Enter your answer rounded to four decimal places.

Answer 1

Let A be the event of obtaining grade A in the course.
Let B be the event that he or she use the lab on a regular basis
Let B' be the event that he or she do not use the lab on a regular basis.

Given that, P(B) = 0.40 and P(B') = 1 - 0.40 = 0.60

P(A | B) = 0.70 and P(A | B') = 0.10

We want to find, P(B | A)

$P(B | A) = \frac { P(A | B) * P(B) }{[ P(A | B) * P(B) ] + [P(A | B') * P(B') ] }$

$=> P(B | A) = \frac { 0.70 *0.40 }{[0.70 *0.40 ] + [0.10*0.60 ] }$

$=> P(B | A) = \frac { 0.28}{[0.28] + [0.06 ] }$

=> P(BA) = 0.28 0.34

Therefore, required probability is 0.8235