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 is a prime number and F = X 4 , then P E ∪ F is

Question

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 is a prime number and F = X 4 , then P E ∪ F is, 0 . 50, 0 . 77, 0 . 35, 0 . 87

MARKS App · Accepted Answer

P E = P 2 or 3 or 5 or 7 = 0.23 + 0.12 + 0.20 + 0.07 = 0.62 P F = P 1 or 2 or 3 = 0.15 + 0.23 + 0.12 = 0.50 P E ∩ F = P 2 o r 3 = 0.23 + 0.12 = 0.35 ∴ P E U F = P E + P F − P E ∩ F = 0.62 + 0.50 − 0.35 = 0.77

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

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