For three events $A,B $ and $C$  ,$P ($ Exactly one of $A$ or $B$ occurs$)\, =\, P ($ Exactly one of $C$ or $A$ occurs $) =$ $\frac{1}{4}$ and $P ($ All the three events occur simultaneously $) =$ $\frac{1}{16}$ Then the probability that at least one of the events occurs is :

The probabilities of three mutually exclusive events are $\frac{2}{3} ,  \frac{1}{4}$ and $\frac{1}{6}$. The statement is

If $A$ and $B$ are two independent events, then $P\,(A + B) = $

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

Given that the events $A$ and $B$ are such that $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ and $P(B)=p .$ Find $p$ if they are independent.