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

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 $A$ and $B$ are two independent events,then the probability of occurrence of at least one of $A$ and $B$ is given by $1 - P(A') P(B')$. Is this statement true or false?

If $A$ and $B$ are mutually exclusive events,$P(A) = \frac{1}{2}$,$P(A \cup B) = \frac{3}{5}$,and $P(B') = p$,then $p = $ . . . . . . .

Two candidates $A$ and $B$ have attended an interview conducted by a recruitment board for two jobs. If the probability that candidate $A$ will get the job is $0.8$ and the probability that candidate $B$ will get the job is $0.7$,then the probability that at least one of them will get the job is

The odds against an event are $5 : 2$ and the odds in favor of another independent event are $6 : 5$. What is the probability that at least one of the events occurs?