Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to

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

Let $S$ be the sample space of all five digit numbers.If $p$ is the probability that a randomly selected number from $S$, is a multiple of $7$ but not divisible by $5$ , then $9\,p$ is equal to.

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

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

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{ k }{2^{15}}$, then $k$ is equal to: