If $A$ and $B$ are mutually exclusive events,then the value of $P(A \cup B)$ is

If $E$ and $F$ are events such that $P(E)=\frac{1}{4}$,$P(F)=\frac{1}{2}$ and $P(E \cap F)=\frac{1}{8}$,find $P(\text{not } E \text{ and not } F)$.

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

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

If $A, B, C$ are three events associated with a random experiment,prove that $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$.

The odds in favour of drawing a king from a pack of $52$ playing cards is