The probability that $A$ speaks truth is $75 \%$ and the probability that $B$ speaks truth is $80 \%$. The probability that they contradict each other when asked to speak on a fact is

If a man throws a die until he gets a number bigger than $3$, then the probability that he gets a $5$ in his last throw is

$12$ balls are distributed among $3$ boxes. The probability that the first box will contain exactly $3$ balls is:

$A$ box contains coupons labelled $1, 2, 3, \ldots, n$. $A$ coupon is picked at random and the number $x$ is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is $y$. Then,the probability that one of the numbers $x, y$ divides the other is (in the options below $[r]$ denotes the largest integer less than or equal to $r$)

The probability that a year chosen at random from the $22^{nd}$ century will have $53$ Sundays is

For two independent events $A$ and $B$,which of the following is true?