If $P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$ and the events $A$ and $B$ are mutually exclusive, then $x = $

If odds against solving a question by three students are $2 : 1 ,  5:2$ and $5:3$ respectively, then probability that the question is solved only by one student is

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is

The odds against a certain event is $5 : 2$ and the odds in favour of another event is $6 : 5$. If both the events are independent, then the probability that at least one of the events will happen is

If $A$ and $B$ are two independent events, then $A$ and $\bar B$ are

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