$A$ and $B$ play $12$ games. $A$ wins $6$ times,$B$ wins $4$ times,and $2$ games are drawn. If $A$ and $B$ play a series of $3$ games,what is the probability that they win alternately?

If four persons are chosen at random from a group of $3$ men,$2$ women and $4$ children,then the probability that exactly two of them are children is:

Three numbers are chosen at random from $1$ to $20$. The probability that the sum of the three numbers is divisible by $3$ is:

From a group of $50$ students,two sections comprising of $20$ and $30$ students are formed. If $Ram$ and $Rahim$ are two particular students among the $50$ students,then the probability that they both belong to the same section is

Two numbers are selected at random from $40$ consecutive natural numbers. What is the probability that the sum of the numbers is odd?

From a group of $10$ men and $5$ women,a four-member committee is to be formed such that it must contain at least one woman. The probability that the committee has more women than men is: