If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A \cup C)$ equals to

The probability of happening at least one of the events $A$ and $B$ is $0.6$. If the events $A$ and $B$ happen simultaneously with a probability of $0.2$,then $P(\bar{A}) + P(\bar{B}) = $

When three identical dice are thrown,what is the probability of getting the same number on each of them?

$A$ 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 $\frac{1}{5}$. If they appear for the interview independently,then the probability that only one of them is selected is:

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is:

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is