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 mutually exclusive.

In an entrance test that is graded on the basis of two examinations,the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?

If $A$ and $B$ are two mutually exclusive events,then $P(A \cup B) = $

The probability that a leap year will have $53$ Fridays or $53$ Saturdays is

If the odds against an event be $2 : 3$,then the probability of its occurrence is

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