Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If $A$ starts the game, then the probability that $B$ wins the game is

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$, then $P(|X-3|<2)=$

If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is