If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}$,$P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$,then $P(A^{\prime} | B)$ is

$A, B$ are the events in a random experiment. If $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(A \cap B)=\frac{1}{4}$, then $P\left(\frac{A^{c}}{B^{c}}\right)+P\left(\frac{A}{B}\right)=$

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one, and $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is:

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

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 $P(\bar{B} \mid \bar{A})=$

If $E$ and $F$ are events such that $P(\overline{F}) = 0.7$ and $P(E \cap F) = 0.2$,then $P(E \mid F)$ is