Cards are drawn one after the other without replacement from a well shuffled pack of cards until and ace card appears. If the probability that exactly 5 cards are drawn before the first ace card appears is $\frac{4}{49}\left(\frac{p_1 \cdot p_2 \cdot p_3}{p_4 \cdot p_5 \cdot p_6}\right),\left(p_i\right.$ is prime, $\left.i=1,2,3,4,5,6\right)$ then $\left(\max \left\{p_i\right\}-\min \left\{p_i\right\}\right)=$

A number is selected at random from the set $\{1,2, \ldots \ldots ., 100\}$. Given that the number selected is divisible 2 , the probability that it is also divisible by 3 or 5 , is

A target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assuming that two direct hits are required to destroy the target completely, the minimum number of bombs to be dropped in order that the probability of destroying the target is not less than $99 \%$, is

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3)=$