Two players $A$ and $B$ alternatively toss $3$ coins simultaneously. The player who gets $2$ heads and $1$ tail first,wins the game. If the game continues until someone wins and if $A$ begins the game,the probability that $B$ wins the game is

Bag $A$ contains $3$ white and $4$ red balls,bag $B$ contains $4$ white and $5$ red balls,and bag $C$ 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

Let the mean and variance of $7$ observations $2, 4, 10, x, 12, 14, y$ (where $x > y$) be $8$ and $16$ respectively. Two numbers are chosen from the set $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement. Then the probability that the smaller number among the two chosen numbers is less than $4$ is:

Three numbers are selected at random from the set ${1, 2, 3, \dots, 8}$ without replacement. Given that the minimum of the selected numbers is $3$ and the maximum is $6$, what is the probability that the third number is $4$ or $5$?

$A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he throws $6$ before $B$ throws $7$,and $B$ wins if he throws $7$ before $A$ throws $6$. If $A$ begins,the probability of $A$ winning is:

There are four machines and it is known that exactly two of them are faulty. They are tested one by one,in a random order until both the faulty machines are identified. The probability that only two tests are needed is: