For $\mathrm{k}=1,2,3$ the box $\mathrm{B}_{\mathrm{k}}$ contains k red balls and $(k+1)$ white balls. Let $P\left(B_1\right)=\frac{1}{2}, P\left(B_2\right)=\frac{1}{3}$ and $\mathrm{P}\left(\mathrm{B}_3\right)=\frac{1}{6} . \mathrm{A}$ box is selected at random and a ball is drawn from it. If a red ball is drawn from it, then the probability that it comes from box $\mathrm{B}_2$ is

A random variable $X$ takes the values $0,1,2,3$, $\qquad$ with probability

$\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1)\left(\frac{1}{5}\right)^x$, where k is a constant.

Then $\mathrm{P}(\mathrm{X}=0)$ is

A fair coin is tossed 99 times. If X is the number of times head occur then $\mathrm{P}[\mathrm{X}=\mathrm{r}]$ is maximum when $\mathrm{r}=$

If X is a binomial variable with range $\{0,1,2,3,4\}$ and $\mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=4)$ then the parameter ' $p$ ' of the binomial distribution is