For any two independent events $E_1$ and $E_2,$ $P\{(E_1 \cup E_2) \cap (\bar{E}_1 \cap \bar{E}_2)\}$ is

If two events $A$ and $B$ are such that $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then $P[B / (A \cup B^c)]$ is equal to

$2$ dice are thrown. Find the probability of getting an odd number on $1$ die and a multiple of $3$ on the other.

$A$ Chartered Accountant applies for a job in $2$ firms $X$ and $Y$. The probability of his being selected in firm $X$ is $0.7$,and being rejected at $Y$ is $0.5$,and the probability of at least $1$ of his applications being rejected is $0.6$. What is the probability that he will be selected in $1$ of the firms?

In a single throw of $2$ dice,find the probability of getting a total of $12$.

An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is