A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is

A drawer contains $5$ brown socks and $4$ blue socks well mixed. A man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match

A box contains $10$ mangoes out of which $4$ are rotten. $2$ mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression

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

A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then the probability that $2$ are white and $1$ is red, is