A bag contains $5$ distinct Red, $4$ distinct Green and $3$ distinct Black balls. Balls are drawn one by one without replacement,then the probability of getting a particular red ball in fourth draw is-

$n$ cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$

Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers with probability of occurrence of $0$ at even places be $\frac{1}{2}$ and probability of occurrence of $0$ at the odd place be $\frac{1}{3}$. Then the probability that $'10'$ is followed by $'01'$ is equal to :

A box contains $10$ mangoes out of which $4$ are rotten. $2$ mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is