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

If $A$ and $B$ are two events of a random experiment such that $P(A \cup B) = 0.65$ and $P(A \cap B) = 0.15$,then $P(\overline{A}) + P(\overline{B}) = $

$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A' \cap B')$.

Let $A$ and $B$ be two independent events. The probability that both $A$ and $B$ occur together is $1/6$ and the probability that neither of them occurs is $1/3$. The probability of occurrence of $A$ is

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:

Three ships $A$, $B$, and $C$ sail from England to India. If the odds in favour of their safe arrival are $2:5$, $3:7$, and $6:11$ respectively, then the probability that exactly two ships arrive safely is