Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$, if $5$ appears on the first

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 $NSS$ but not $NCC$.

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random Find the probability that she reads neither Hindi nor English newspapers.

Events $E$ and $F$ are such that $P ( $ not  $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $