The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{{10}},\,\frac{3}{5}$ and $\frac{1}{4}.$ The probability that the student fails in the examination is

If $E$ and $F$ are events with $P\,(E) \le P\,(F)$ and $P\,(E \cap F) > 0,$ then

The chance of throwing a total of $7$ or $12$ with $2$ dice, is

A bag contains $3$ white and $2$ black balls and another bag contains $2$ white and $4 $ black balls. A ball is picked up randomly. The probability of its being black is

Three coins are tossed once. Find the probability of getting $3$ tails.

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 ?