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

Three critics review a book. For the three critics,the odds in favor of the book are $2:5$,$3:4$,and $4:3$ respectively. The probability that the majority is in favor of the book is given by

If $A$ and $B$ are two events in a random experiment such that $P(A) + P(B) = 2 P(A \cap B)$, then:

One card is drawn randomly from a pack of $52$ cards. The probability that it is a king or a spade 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 the events $A$ and $B$ are independent.