If the probability of $X$ to fail in the examination is $0.3$ and that for $Y$ is $0.2$,then the probability that either $X$ or $Y$ fail in the examination is

An event has odds in favour $4 : 5$. Then,the probability that the event occurs is:

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

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

Two candidates $A$ and $B$ have attended an interview conducted by a recruitment board for two jobs. If the probability that candidate $A$ will get the job is $0.8$ and the probability that candidate $B$ will get the job is $0.7$,then the probability that at least one of them will get the job is

$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A \cup B)$.