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

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.

$A$ random variable $X$ has the probability distribution:

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,then $P(E \cup F)$ is

$A$ person $P$ speaks the truth in $75\%$ of cases and another person $R$ in $80\%$ of cases. What is the probability that they are likely to contradict each other in narrating the same event?

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

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