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

An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

In a single throw of two dice, the probability of getting more than $7$ is

‘$A$’ draws two cards with replacement from a pack of $52$ cards and ‘$B$' throws a pair of dice what is the chance that ‘$A$’ gets both cards of same suit and ‘$B$’ gets total of $6$

Let $E _{1}, E _{2}, E _{3}$ be three mutually exclusive events such that $P \left( E _{1}\right)=\frac{2+3 p }{6}, P \left( E _{2}\right)=\frac{2- p }{8}$ and $P \left( E _{3}\right)$ $=\frac{1- p }{2}$. If the maximum and minimum values of $p$ are $p _{1}$ and $p _{2}$, then $\left( p _{1}+ p _{2}\right)$ is equal to.

$2$ boys and $2$ girls are in Room $X$, and $1$ boy and $3$ girls in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.