If $P(A) = \frac{6}{11}$,$P(B) = \frac{5}{11}$ and $P(A \cup B) = \frac{7}{11}$,find $P(A | B)$.

Two persons $P$ and $Q$ are considering applying for a job. The probability that $P$ applies for the job is $1/4$,the probability that $P$ applies for the job given that $Q$ applies for the job is $1/2$,and the probability that $Q$ applies for the job given that $P$ applies for the job is $1/3$. Then the probability that $P$ does not apply for the job given that $Q$ does not apply for the job is

Four fair dice $D_1, D_2, D_3$ and $D_4$,each having six faces numbered $1, 2, 3, 4, 5$ and $6$,are rolled simultaneously. The probability that $D_4$ shows a number appearing on at least one of $D_1, D_2$ and $D_3$ is

If $A$ and $B$ are events such that $P(A) > 0$ and $P(B) \neq 1$,then $P(A \mid B^{\prime}) = $ . . . . . . .

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

If events $A$ and $B$ are such that $P(A) = \frac{1}{4}$, $P(A \cap B) = \frac{1}{10}$ and $P(A|B) = 2P(B|A)$, then $P(B) = ..........$