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 $B$ an two events such that $P\,(A \cup B) = \frac{5}{6}$,$P\,(A \cap B) = \frac{1}{3}$ and $P\,(\bar B) = \frac{1}{3},$ then $P\,(A) = $

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

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$ then the probability of both of them occur together is

Three athlete $A, B$ and $C$ participate in a race competetion. The probability of winning $A$ and $B$ is twice of winning $C$. Then the probability that the race win by $A$ or $B$, is

Let $A$ and $B$ are two events and $P(A') = 0.3$, $P(B) = 0.4,\,P(A \cap B') = 0.5$, then $P(A \cup B')$ is