If $A$ and $B$ are two events in a random experiment such that $P(A) + P(B) = 2 P(A \cap B)$, then:

If $A$ and $B$ are two events with $P(A \cap B) = \frac{1}{3}$,$P(A \cup B) = \frac{5}{6}$,and $P(A^C) = \frac{1}{2}$,then the value of $P(B^C)$ is

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

For two given events $A$ and $B$,$P(A \cap B)$ is:

The probabilities that $A$ and $B$ speak the truth are $\frac{4}{5}$ and $\frac{3}{4}$ respectively. The probability that they contradict each other when asked to speak on a fact is

If the odds against $A$ solving a problem are $4:3$ and the odds in favor of $B$ solving the problem are $7:5$,what is the probability that only one of them solves the problem?