‘$X$’ speaks truth in $60\%$ and ‘$Y$’ in $50\%$ of the cases. The probability that they contradict each other narrating the same incident 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 number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$  is. . . . . . 

If any four numbers are selected and they are multiplied, then the probability that the last digit will be $1, 3, 5$ or $7$ is

A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?

A bag contains $3$ white, $3$ black and $2$ red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is