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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:X is prime number} and F = {X:X < 4}, then the probability $P (E \cup F)$ is

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0.35

0.77

0.87

0.50

answer is B.

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Detailed Solution

Required probability
$= P (E \cup F) = P ({1, 2, 3} \cup {2, 3, 5, 7}) = P ({1, 2, 3, 5, 7})$
$= P (1) + P (2) + P (3) + P (5) + P (7) = 0.15 + 0.23 + 0.12 + 0.20 + 0.07 = 0.77$

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