A word consists of $11$ letters in which there are $7$ consonants and $4$ vowels. If $2$ letters are chosen at random, then the probability that all of them are consonants, is

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

From a well shuffled pack of $52$ playing cards, cards are drawn one by one with replacement. Probability that $5^{th}$ card will be "king of hearts" is

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

A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, is

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is