# probability question

a class of 60 students, 15 students failed in exam A, 25 students failed in exam B ,8 students failed in both , what is the probability of a student passing A and failing B ?

when I solve it using Venn diagrams the probability is 17/60

but when I solve it using P(Passing A & failing B)=P(A' intersection B)=P(A')*P(B) the result =18.75/60

shouldn't the two events be mutually exclusive (independent) ,passing A shouldn't affect passing B and vice versa so the intersection equals their product, so what is it that I'm doing wrong ?

• I think you mean to ask either "what proportion of students passed exam A but failed B" or "if a student is selected uniformly at random, what is the probability that he will have passed A and failed B". We have no business predicting the future. – nullUser Jun 5 '13 at 14:29
• @nullUser ,Ross Millikan &amWhy :thank you. – Oz Le Jun 5 '13 at 15:10

More than half the students who failed test A also failed test B. But less than $1/3$ of the students who failed B, also failed A. So performance in A is not independent of performance in B. For that reason, we cannot use the "formula" you tested, would be valid to use only if the events were independent.