If $A$ and $B$ are two events such that $P(B) \neq 0$ and $P(B) \neq 1$,then $P(\bar{A} \mid \bar{B})$ is equal to:

Bag $A$ contains $9$ white and $8$ black balls,while bag $B$ contains $6$ white and $4$ black balls. One ball is randomly picked up from bag $B$ and mixed with the balls in bag $A$. Then a ball is randomly drawn from bag $A$. If the probability that the ball drawn is white is $p/q$ (where $gcd(p,q)=1$),then $p+q$ is equal to:

If $P(E)=0.8, P(F)=0.5$ and $P(F \mid E)=0.4$ then,$P(E \mid F)=$ . . . . . . .

In a group of $14$ males and $6$ females,$8$ males and $3$ females are aged above $40 \text{ yr}$. The probability that a person selected at random from the group is aged above $40 \text{ yr}$,given that the selected person is a female,is:

$A$ 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

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.