The probability of getting a number greater than $2$ in throwing a die is

If two subsets $A$ and $B$ are selected at random from a set $S$ containing $n$ elements,then the probability that $A \cap B = \phi$ and $A \cup B = S$ is

$A$ man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

If in a lottery there are $5$ prizes and $20$ blanks,then the probability of getting a prize is

The probability that a non-leap year selected at random will contain $52$ Saturdays or $53$ Sundays is

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.