Let $\mathrm{X}$ and $\mathrm{Y}$ be two events such that $\mathrm{P}(\mathrm{X})=\frac{1}{3}, \mathrm{P}(\mathrm{X} \mid \mathrm{Y})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{Y} \mid \mathrm{X})=\frac{2}{5}$. Then

$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$   $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$    $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$    $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$

Three coins are tossed. Describe Three events which are mutually exclusive but not exhaustive.

Three coins are tossed together, then the probability of getting at least one head is

A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

A box contains $3$ white and $2$ red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is

If $A$ and $B$ are mutually exclusive events, then the value of $P (A$ or $B$) is