Question 1176403
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.
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pass fail total
67.5/7.5--75
5---20--25
72.5--27.5-100
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given they passed (72.5) the probability they studied was 67.5/72.5 or 0.93.