If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B \mid A \cup \bar{B})=$

An urn $A$ contains $3$ white and $5$ black balls. Another urn $B$ contains $6$ white and $8$ black balls. $A$ ball is picked from $A$ at random and then transferred to $B$. Then, a ball is picked at random from $B$. The probability that it is a white ball is

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

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$,given that $5$ appears on the first die?

If $6 P(A) = 8 P(B) = 14 P(A \cap B) = 1$,then $P(A' \mid B) = $ . . . . . . .

If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A \cap B) = \frac{3}{20}$,then the conditional probability $P(A | A' \cup B')$,where $A'$ denotes the complement of $A$,is equal to: