In a class of $60$ students, $30$ opted for $NCC$ , $32$ opted for $NSS$ and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random, find the probability that The student has opted neither $NCC$ nor $NSS$.

One bag contains $5$ white and $4$ black balls. Another bag contains $7$ white and $9$ black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is

Let $A$ and $B$ be two events such that $P\overline {(A \cup B)} = \frac{1}{6},P(A \cap B) = \frac{1}{4}$ and $P(\bar A) = \frac{1}{4},$ where $\bar A$ stands for complement of event $A$. Then events $A$ and $B$ are

If $A$ and $B$ are two events such that $P\,(A \cup B)\, + P\,(A \cap B) = \frac{7}{8}$ and $P\,(A) = 2\,P\,(B),$ then $P\,(A) = $

In a horse race the odds in favour of three horses are $1:2 ,  1:3$ and $1:4$. The probability that one of the horse will win the race is