Let $A$ be the event that the absolute difference between two randomly choosen 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 card is drawn from a pack of $52$ cards. If $A =$ card is of diamond, $B =$ card is an ace and $A \cap B = $ card is ace of diamond, then events $A$ and $B$ are

A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is

The chance of India winning toss is $3/4$. If it wins the toss, then its chance of victory is $4/5$ otherwise it is only $1/2$. Then chance of India's victory is

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment

$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
$C:$ $^{\prime}$the sum is less than $4 $$^{\prime}$
$D:$ $^{\prime}$the sum is greater than $11$$^{\prime}$.

Which pairs of these events are mutually exclusive ?

A die has two faces each with number $^{\prime}1^{\prime}$ , three faces each with number $^{\prime}2^{\prime}$ and one face with number $^{\prime}3^{\prime}$. If die is rolled once, determine $P($ not $3)$