If A, B and C are mutually exclusive and exhaustive events and it is known that $P(A\cup B)=0.63$, calculate P(C).

A and B are two candidates seeking admission in an engineering college. The probability that A is selected is $0.5$ and the probability that both are selected is at most  $0.3.$ Is it possible that the probability of B getting selected is $0.7?$

In a class of $60$ students, $30$ opted for Mathematics,  $32$ opted for Biology and $24$ opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that:

The student opted for Mathematics or Biology.

In a class of $60$ students, $30$ opted for Mathematics,  $32$ opted for Biology and $24$ opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that:

The student has opted neither Mathematics nor Biology.

In a class of $60$ students, $30$ opted for Mathematics,  $32$ opted for Biology and $24$ opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that:

The student has opted Mathematics but not Biology.