$A, B, C$ are three events,one of which must and only one can happen. The odds in favour of $A$ are $4:6$,and the odds against $B$ are $7:3$. Then,the odds against $C$ are:

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 $P(E \cup F)$.

If the odds in favour of an event be $3 : 5$,then the probability of non-occurrence of the event is

Given that the events $A$ and $B$ are such that $P(A) = \frac{1}{2}$,$P(A \cup B) = \frac{3}{5}$,and $P(B) = p$. Find $p$ if they are mutually exclusive.

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?

The probabilities of two events $A$ and $B$ occurring are $0.25$ and $0.50$ respectively. The probability of both events occurring simultaneously is $0.12$. Find the probability that neither event occurs.