$A$ bag contains $3$ black and $4$ white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white,is

If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is

If $A$ and $B$ are two events of a sample space $S$ such that $P(A)=0.2$,$P(B)=0.6$ and $P(A \mid B)=0.5$,then $P(A^{\prime} \mid B) = $

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) = $

$A$ and $B$ are two groups of books. Group $A$ consists of $8$ science and $5$ engineering books, and group $B$ consists of $6$ science and $7$ engineering books. When an unbiased die is rolled, if $2$ or $5$ turns up, a book is selected at random from group $A$. Otherwise, a book is selected at random from group $B$. The probability of selecting a science book is

If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6$,$P(B)=0.3$,and $P(A \mid B)=0.5$,then $P(\bar{B} \mid \bar{A})=$