The probability that a man and his wife will be alive after $20 \text{ years}$ are $\frac{1}{4}$ and $\frac{1}{3}$ respectively. The probability that neither the man nor his wife will be alive after $20 \text{ years}$ is

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0, 60]$ is less than or equal to $a$. If $P(A) = \frac{11}{36}$,then $a$ is equal to $...............$.

$A$ box $P$ contains one white ball,three red balls and two black balls. Another box $Q$ contains two white balls,three red balls and four black balls. If one ball is drawn at random from each one of the two boxes,then the probability that the balls drawn are of different colour is

$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by $3$ is

Boxes $B_1, B_2$,and $B_3$ contain balls as given below:

Box	White	Black
$B_1$	$1$	$2$
$B_2$	$3$	$1$
$B_3$	$2$	$3$

One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is

Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{1}{3}$,$\frac{1}{4}$,and $\frac{1}{5}$,then the probability that none of them can solve it is: