$A$ and $B$ appear for an interview for two vacancies in the same post. The probability of $A’s$ selection is $\frac{1}{6}$ and that of $B’s$ selection is $\frac{1}{4}$. Find the probability that only one of them is selected.

$A$ and $B$ appear for an interview for two vacancies in the same post. The probability of $A’s$ selection is $\frac{1}{6}$ and that of $B’s$ selection is $\frac{1}{4}$. Find the probability that none is selected.

(Write answer in lowest fraction form)

$A$ and $B$ appear for an interview for two vacancies in the same post. The probability of $A’s$ selection is $\frac{1}{6}$ and that of $B’s$ selection is $\frac{1}{4}$. Find the probability that at least one of them is selected.

(Write answer in fraction form)

Given the probability that $A$can solve a problem is $\frac{2}{3}$, and the probability that $B$ can solve the same problem is $\frac{3}{5}$, find the probability that at least one of $A$ and $B$ will solve the problem.

(Write answer in fraction form)

Given the probability that $A$can solve a problem is $\frac{2}{3}$, and the probability that $B$ can solve the same problem is $\frac{3}{5}$, find the probability that none of the two will solve the problem.

(Correct your answer two decimal places)

The probabilities of $A, B, C$ solving a problem are $\frac{1}{3}, \frac{1}{4}\mathrm{and} \frac{1}{6}$, respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.

(Write answer in fraction form)

$$$A$ can hit a target $4$ times in $5$ shots, $B$ can hit $3$ times in $4$ shots, and $C$ can hit $2$ times in $3$ shots. Calculate the probability that $A,B$ and $C$ all hit the target.

(Write answer in fraction form)

$A$ can hit a target $4$ times in $5$ shots, $B$ can hit $3$ times in $4$ shots, and $C$ can hit $2$ times in $3$ shots. Calculate the probability that

$B$ and $C$ hit and $A$ does not hit target.

(Write answer in fraction form).