In a lottery $50$ tickets are sold in which $14$ are of prize. A man bought $2$ tickets, then the probability that the man win the prize, is

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

There are $n$ letters and $n$ addressed envelops. The probability that each letter takes place in right envelop is

A box contains $25$ tickets numbered $1, 2, ....... 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is

The probability, that in a randomly selected $3-$digit number at least two digits are odd, 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