Three persons $P, Q$ and $R$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is

The probability that a randomly selected $2$-digit number belongs to the set $\{n \in N : (2^{n}-2) \text{ is a multiple of } 3\}$ is equal to:

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:
$A:$ the sum is even.
$B:$ the sum is a multiple of $3$.
$C:$ the sum is less than $4$.
$D:$ the sum is greater than $11$.
Which pairs of these events are mutually exclusive?

$A$ bag contains $4$ white,$5$ black and $6$ red balls. If a ball is drawn at random,then what is the probability that the drawn ball is either white or red?

If a number is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$,then the probability that the chosen number is a perfect cube is

$A$ problem in Mathematics is given to three students $A, B, C$ and their respective probabilities of solving the problem are $\frac{1}{2}, \frac{1}{3},$ and $\frac{1}{4}$. What is the probability that the problem is solved?