Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$, $P(B) = 0.4$, and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

If $2 P(A) = P(B) = \frac{5}{13}$ and $P(A \mid B) = \frac{2}{5}$,then $P(A \cup B) = $ . . . . . . .

If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E|F)-P(F|E)$ equals

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?

Two dice are thrown simultaneously. If $A$ is the event of getting the sum of the numbers on two dice as greater than or equal to $8$ and $B$ is the event of getting a number less than or equal to $3$ on at least one of the dice. Then,$P(B / A) = $

Let $E^{C}$ denote the complement of an event $E$. Let $E_{1}, E_{2}$ and $E_{3}$ be any pairwise independent events with $P(E_{1}) > 0$ and $P(E_{1} \cap E_{2} \cap E_{3}) = 0$. Then $P(E_{2}^{C} \cap E_{3}^{C} / E_{1})$ is equal to