If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$,and $P(A \cap B) = \frac{1}{4}$,then find the value of $P(A' \cap B')$.

The probabilities of three mutually exclusive events are $\frac{2}{3}$,$\frac{1}{4}$,and $\frac{1}{6}$. The statement is:

Three ships $A, B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2 : 5, 3 : 7$ and $6 : 11$ respectively,then the probability of all the ships arriving safely is:

Suppose that $A, B, C$ are events such that $P(A) = P(B) = P(C) = \frac{1}{4}$,$P(AB) = P(CB) = 0$,and $P(AC) = \frac{1}{8}$. Then find $P(A \cup B)$.

If $A$ and $B$ are two mutually exclusive events,then $P(A \cup B) = $

$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is