A random variable X has the following probability distribution

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

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

The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......

The centers for disease control have determined that when a person is given a vaccine, the probability that the person will develop immunity to a virus is $0.8$. If $8$ people are given this vaccine, then the probability that exactly $4$ will develop immunity is...

The Variance of the following probability distribution of X is

X	$0$	$1$	$2$	$3$
P(X)	$q^3$	$3q^2 p$	$3qp^2$	$p^3$

where $0 < p < 1, q = 1 - p$