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 ?
$A$ and $B$
$A$ and $D$
$B$ and $D$
$C$ and $D$
A problem of mathematics is given to three students whose chances of solving the problem are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$ respectively. The probability that the question will be solved is
A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $3$.
From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is
In a throw of three dice, the probability that at least one die shows up $1$, is
In each of the following experiments specify appropriate sample space A person is noting down the number of accidents along a busy highway during a year.