There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

All the spades are taken out from a pack of cards.From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace of spade comes in the $4^{th}$ draw is

If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks, then his chance of winning prize are

A bag contains $4$ white, $5$ red and $6$ black balls. If two balls are drawn at random, then the probability that one of them is white is

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$, respectively. Suppose $\alpha$ is the number of heads that appear when $C _1$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C _2$ is tossed twice, independently, Then probability that the roots of the quadratic polynomial $x^2-\alpha x+\beta$ are real and equal, is

Two different families $A$ and $B$  are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket . If the probability that all the tickets go to the children of the family $B$ is $\frac {1}{12}$ , then the number of children in each family is?