Three vertices are chosen randomly from the seven vertices of a regular $7$ -sided polygon. The probability that they form the vertices of an isosceles triangle is

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them 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

Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

A committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in committee, is

If four persons are chosen at random from a group of $3$ men, $2$ women and $4 $ children. Then the probability that exactly two of them are children, is