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(B) Given the events:$E = \{X 	ext{ is a prime number}\} = \{2, 3, 5, 7\}$$F = \{X < 4\} = \{1, 2, 3\}$Calculating probabilities:$P(E) = P(2) + P(3)

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$0.77$

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(B) Given the events:$E = \{X 	ext{ is a prime number}\} = \{2, 3, 5, 7\}$$F = \{X Calculating probabilities:$P(E) = P(2) + P(3) + P(5) + P(7) = 0.23 + 0.12 + 0.20 + 0.07 = 0.62$$P(F) = P(1) + P(2) + P(3) = 0.15 + 0.23 + 0.12 = 0.50$Intersection of events:$E \cap F = \{X 	ext{ is a prime number and } X $P(E \cap F) = P(2) + P(3) = 0.23 + 0.12 = 0.35$Using the addition rule for probability:$P(E \cup F) = P(E) + P(F) - P(E \cap F)$$P(E \cup F) = 0.62 + 0.50 - 0.35 = 0.77$

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

$X=x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$?

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

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$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$? $X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$