The probability of hitting a target by three marksmen are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously,is

Three $6$-faced dice are thrown together. The probability that no two dice show the same number on them is

$A$ card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king?

Two dice are thrown. Find the probability of getting at least one of the two numbers as $4$.

$A$ husband and wife appear in an interview for $2$ vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's is $\frac{1}{5}$. What is the probability that none of them will be selected?

There are $3$ bags which are known to contain $2$ white and $3$ black balls; $4$ white and $1$ black balls and $3$ white and $7$ black balls respectively. $A$ ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is