The number of trials conducted in a binomial distribution is 6 . If the difference between the mean and variance of this variate is $\frac{27}{8}$, then the probability of getting atmost 2 successes 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 $P(X \leq 3)=$

A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. If one fruit is picked out at random from each basket, then the probability of getting one apple and one orange is

Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is a queen, then the probability of getting a face card from a black suit in the second draw is