Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X),$ with replacement, then the probability that $A$ and $B$ have equal number elements, is

A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, is

From a well shuffled pack of $52$ playing cards, cards are drawn one by one with replacement. Probability that $5^{th}$ card will be "king of hearts" is

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee