One die has two faces marked $1$ , two faces marked $2$ , one face marked $3$ and one face marked $4$ . Another die has one face marked $1$ , two faces marked $2$ , two faces marked $3$ and one face marked $4$. The probability of getting the sum of numbers to be $4$ or $5$ , when both the dice are thrown together, is

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

A box contains $15$ tickets numbered $1, 2, ....... 15$. Seven tickets are drawn at random one after the other with replacement. The probability that the greatest number on a drawn ticket is $9$, is

Mr. A has six children and atleast one child is a girl, then probability that Mr. A has $3$ boys and $3$ girls, is 

In a lottery, a person choses six different natural numbers at random from $1$ to $20$ , and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [ Hint order of the numbers is not important.]

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