A bag contains $16$ coins of which two are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is

Five numbers $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ are randomly selected from the numbers $1,2,3, \ldots \ldots, 18$ and are arranged in the increasing order $\left( x _{1}< x _{2}< x _{3}< x _{4}< x _{5}\right)$. The probability that $x_{2}=7$ and $x_{4}=11$ is

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral 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

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is