A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is choosen at random. The probability that this pencil is not defective is

A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white 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 bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is at least one pair is equal to

A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-

A committee consists of $9$ experts taken from three institutions $A, B$ and $C$, of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign, then the probability that they belong to different institutions is