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}) = $

Let $A$ and $B$ be two events such that $P(A) = 0.3$ and $P(A \cup B) = 0.8$. If $A$ and $B$ are independent events,then $P(B) = $

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

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:

If a card is drawn at random from a well-shuffled pack of $52$ playing cards,then the probability that it is either an ace or a spade card is

If $A$ and $B$ are events such that $P(A \cup B) = \frac{5}{6}$, $P(\bar{A}) = \frac{1}{4}$, and $P(B) = \frac{1}{3}$, then $A$ and $B$ are