If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of number $\{1,2,3, \ldots \ldots 10\}$. Then, the probability that $\left|x^2-y^2\right|$ is divisible by 6 is

Bag $A$ contains 3 white and 4 red balls, bag $B$ contains 4 white and 5 red balls and bag $C$ is contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is

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