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

For any two events $A$ and $B$,if $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$,then $3a + 2b + 5c = ?$

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years is:

The probabilities of two events $A$ and $B$ occurring are $0.25$ and $0.50$ respectively. The probability of both events occurring simultaneously is $0.12$. Find the probability that neither event occurs.

If $A$ and $B$ are two events such that $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$ and $P(\bar{B}) = \frac{1}{3}$,then $P(A) = $

Three critics review a book. For the three critics,the odds in favor of the book are $2:5$,$3:4$,and $4:3$ respectively. The probability that the majority is in favor of the book is given by