A random variable X has the probability distribution

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

for the events E = {X is a prime number} and F = {X $\leq$ 3}, then P (E$\cup$F)=

The event $E$ is that $X$ is a prime number. From the given values, the prime numbers are $2, 3, 5, 7$.

$E = \{2, 3, 5, 7\}$

The event $F$ is that $X \leq 3$. From the given values, the numbers less than or equal to $3$ are $1, 2, 3$.

$F = \{1, 2, 3\}$

The union of events $E$ and $F$ is:

$E \cup F = \{1, 2, 3, 5, 7\}$

The probability $P(E \cup F)$ is the sum of the probabilities of these individual outcomes:

$P(E \cup F) = P(X=1) + P(X=2) + P(X=3) + P(X=5) + P(X=7)$

Substituting the values from the probability distribution table:

$P(E \cup F) = 0.23 + 0.15 + 0.12 + 0.20 + 0.08$

$P(E \cup F) = 0.78$

Answer: $0.78$