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
$\frac{1}{3}$
$\frac{8}{{15}}$
$\frac{5}{{18}}$
$\frac{2}{3}$
$n$ 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 purse contains $4$ copper coins $\& \, 3$ silver coins, the second purse contains $6$ copper coins $\& \,2$ silver coins. If a coin is drawn out of one of these purses, then the probability that it is a copper coin is :-
The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :
A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is
From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is