If $A$ and $B$ are arbitrary events,then

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 = $ . . . . . . .

If $P(A \cup B) = 0.8$ and $P(A \cap B) = 0.3,$ then $P(\bar A) + P(\bar B) = $

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?

If a number is selected from the first $30$ natural numbers,then the probability that the number selected is divisible by $4$ or $7$ is:

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occur simultaneously is $0.16$. Then the probability that none of the two occurs is