If $X$ and $Y$ are two independent binomial variates,satisfying $B(10, 1/2)$ and $B(8, 1/2)$ respectively,then the probability $P(X + Y = 2)$ is

The records of a hospital show that $10\%$ of the cases of a certain disease are fatal. If $6$ patients are suffering from the disease,then the probability that only three will die is

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$,then $k$ is equal to:

If $X$ is a binomial variate with mean $6$ and variance $2$,then the value of $P(5 \leq X \leq 7)$ is

$A$ man takes a step forward with probability $0.4$ and backward with probability $0.6$. The probability that at the end of eleven steps he is one step away from the starting point is

$A$ fair coin is tossed $99$ times. If $X$ is the number of times head occurs,then $P[X=r]$ is maximum when $r=$