Question

Among the examinees in an examination 30%, 35% and 45% failed in Statistics, in Mathematics, and in at least one of the subjects respectively. An examinee is selected at random. Find the probabilities that
a. He failed in Mathematics only
b. He passed in Statistics, if it is known that he has failed in Mathematics

Answer 1

P(S and M) = P(S) + P(M) - P(S or M)
= .3 + .35 - .45
= .2

You could now make a Venn Diagram with two overlapping circles called S and M
Enter .2 into the overlap ( the P(S and M) )
since S must be .3 and .2 is already accounted for, the part of ONLY S would be .1
in the same way the part of M only would be .15

Answer 2

good