$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is
$P(A) = P(\bar A)$
$P\,(A \cap B) = P(A' \cap B')$
$P\,(A) = P\,(B)$
None of these
Three persons $P, Q$ and $R$ independently try to hit a target . If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $P$ or $Q$ but not by $R$ is
If ${A_1},\,{A_2},...{A_n}$ are any $n$ events, then
Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is
Given $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$. Find $P(A $ or $B),$ if $A$ and $B$ are mutually exclusive events.
If the odds against an event be $2 : 3$, then the probability of its occurrence is