$A$ 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?

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is

Four cards are drawn one by one from a well-shuffled pack of $52$ cards. What is the probability that all four cards belong to the same suit?

Out of a group of $10$ people,there are $5$ lawyers,$3$ doctors,and $2$ engineers. If $4$ people are selected at random,what is the probability that at least one person from each profession is included?

Two friends $A$ and $B$ have an equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to the daughters of $A$ is $1/20$. The number of daughters each of them has is:

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6\}$. If the probability of this equation having two distinct real roots is $p$,then $216p$ equals: