In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

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

A binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn 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?

Two numbers are selected randomly from the set $S = \{ 1,\,2,\,3,\,4,\,5,\,6\} $ without replacement one by one. The probability that minimum of the two numbers is less than $4$ is