If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ $P(\bar A) = 2/3,$ then $P(\bar A \cap B)$ is
$\frac{5}{{12}}$
$\frac{3}{8}$
$\frac{5}{8}$
$\frac{1}{4}$
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
A coin is tossed twice. If events $A$ and $B$ are defined as :$A =$ head on first toss, $B = $ head on second toss. Then the probability of $A \cup B = $
In a horse race the odds in favour of three horses are $1:2 , 1:3$ and $1:4$. The probability that one of the horse will win the race is
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that both balls are red.
If $A$ and $B$ are arbitrary events, then