Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu $$.

The standard deviation for this distribution is given by

If $$P(X)$$ $$ = $$ $$1/4,$$ $$P(Y) = 1/3,$$ and $$\,\,P\left( {X \cap Y} \right) = 1/12,\,\,$$ the value of $$P(Y/X)$$ is

The probability of obtaining at least two $$'SIX'$$ in throwing a fair dice $$4$$ times is

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $$1/6$$ and that of Ramesh is $$1/8$$. What is the probability that only one of them will be selected?