If the probability for $A$ to fail in an exam is $0.2$ and that for $B$ is $0.3$,then the probability that either $A$ or $B$ fails is $\leq \ldots \ldots$.

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

The probabilities that $A$ and $B$ speak the truth are $\frac{4}{5}$ and $\frac{3}{4}$ respectively. The probability that they contradict each other when asked to speak on a fact is

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) = $

If the probability of an event occurring is $3:8$,what is the probability of the event not occurring?

The odds against a certain event is $5 : 2$ and the odds in favour of another event is $6 : 5$. If both the events are independent,then the probability that at least one of the events will happen is