If six students, including two particular students $A$ and $B,$ stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is
$\frac {8}{15}$
$\frac {4}{15}$
$\frac {2}{15}$
$\frac {1}{15}$
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is
Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?
A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is
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
Two dice are thrown $5$ times, and each time the sum of the numbers obtained being $5$ is considered a success. If the probability of having at least $4$ successes is $\frac{\mathrm{k}}{3^{11}}$, then $\mathrm{k}$ is equal to