An anti aircraft gun take four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are $0.4, 0.3, 0.2$ and $0.1$ respectively. The probability that the gun hit the plane is :-

From a book containing $100$ pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is $11$, is

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

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

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 :  $A^{\prime}$, $B^{\prime}, C$ are mutually exclusive and exhaustive.

A box contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black, $4$ white and $3$ red is