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

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.

Two events $A$ and $B$ will be independent, if

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

$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

If the probability of $X$ to fail in the examination is $0.3$ and that for $Y$ is $0.2$, then the probability that either $X$ or $Y$ fail in the examination is