SOLUTION: A test on probability is to be given next week. Suppose 75 percent of the students study for the test and 25 percent do not. If a student studies for the exam, the probability that

Click here to see ALL problems on Probability-and-statistics

Question 1176403: A test on probability is to be given next week. Suppose 75 percent of the students study for the test and 25 percent do not. If a student studies for the exam, the probability that he or she will pass is 0.90. If the student does not study, the probability that he or she will pass is 20 percent. Given that the student passed the test, what is the probability he or she studied?

I would like to be told how to do this problem broken down
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Let the probability of passing the test=B
Let the probability of having studied=A
Bayes' Theorem
P(A|B)=P(B|A)*P(A)/P(B)
=0.90*0.75/0.725
=0.93
The issue is what per cent of people passed the test overall? That is 0.75*90+0.25*20=0.725.
-
pass fail total
67.5/7.5--75
5---20--25
72.5--27.5-100
-
given they passed (72.5) the probability they studied was 67.5/72.5 or 0.93.