The probabilities of solving a specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently,find the probability that exactly one of them solves the problem.

There are two children in a family. The probability that both of them are boys is

$A$ box contains $100$ tickets numbered $1$ to $100$. $A$ ticket is drawn at random from the box. Then the probability that the number on the ticket is a perfect square is

There are $3$ families,each having $1$ boy and $1$ girl. If one child is selected from each family,what are the elements of the event that only girls are selected?

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive and exhaustive.

$A, B$ and $C$ are mutually exclusive events. If $P(A) = \frac{3x + 1}{3}$,$P(B) = \frac{1 - x}{4}$,and $P(C) = \frac{1 - 2x}{2}$,then the possible values of $x$ lie in the interval ...