$A$ fair coin is tossed repeatedly. If a tail appears on the first four tosses,then the probability of a head appearing on the fifth toss equals:

The probability of solving a problem by three persons $A, B$ and $C$ independently is $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability that the problem is solved by exactly two of them is

If $A, B,$ and $C$ can hit a target $4$ out of $5$ times,$3$ out of $4$ times,and $2$ out of $3$ times respectively,what is the probability that exactly two of them hit the target?

What is the probability of having $53$ Sundays in a non-leap year?

The probability of choosing randomly a number $c$ from the set $\{1, 2, 3, \ldots, 9\}$ such that the quadratic equation $x^2 + 4x + c = 0$ has real roots is

$A$ fair coin and an unbiased die are tossed. Let $A$ be the event 'head appears on the coin' and $B$ be the event '$3$ on the die'. Check whether $A$ and $B$ are independent events or not.