In a box, there are $20$ cards, out of which $10$ are lebelled as $\mathrm{A}$ and the remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A-$card is obtained. The probability that the second $A-$card appears before the third $B-$card is

- [JEE MAIN 2020]

- A
$\frac{11}{16}$

- B
$\frac{13}{16}$

- C
$\frac{9}{16}$

- D
$\frac{15}{16}$

If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :

- [JEE MAIN 2015]

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to through $9$ from both dice will be avoided the prize. If $A$ throws first then the probability that $B$ wins the game is

A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is

From a class of $12$ girls and $18$ boys, two students are chosen randomly. What is the probability that both of them are girls

From a group of $7$ men and $4$ ladies a committee of $6$ persons is formed, then the probability that the committee contains $2$ ladies is