If $A$ and $B$ are two non-mutually exclusive events such that $P(A \mid B) = P(B \mid A)$,then

Two planes $I$ and $II$ drop bombs on a target. The probabilities of hitting the target by $I$ and $II$ are $0.3$ and $0.2$ respectively. The second plane drops the bomb only if the first plane fails to hit the target. What is the probability that the second plane hits the target?

If two unbiased dice are rolled simultaneously until a sum of the numbers appearing on these dice is either $7$ or $11$, then the probability that $7$ comes before $11$ is:

Prove that if $E$ and $F$ are independent events,then so are the events $E$ and $F^{\prime}$.

$A$ number is selected at random from the set $\{1, 2, \ldots, 100\}$. Given that the selected number is divisible by $2$, what is the probability that it is also divisible by $3$ or $5$?

For two events $A$ and $B$,$P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .