Two natural numbers are chosen at random from 1 to 100 and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by 4 , then $P(A \cap \bar{B})=$

A box $P$ contains one white ball, three red ball and two black balls. Another box $Q$ contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different colour is

A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

For a binomial variate $X \sim B(n, p)$ the difference between the mean and variance is 1 and the difference between their square is 11 . If the probability of $P(x=2)=m\left(\frac{5}{6}\right)^n$ and $n=36$, then $m: n$