$A$ party of $23$ persons take their seats at a round table. The odds against two specific persons sitting together are

If $P(A) = \frac{1}{4}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A \cap 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 $P(A' \cap B')$.

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

$A, B, C$ 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:

Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$. Find $P(\text{neither } A \text{ nor } B)$.