Question

A random variable X has the probability distribution :

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

• A. 0.50
• B. 0.77
• C. 0.35
• D. 0.87

Answer 1

Answer: (B)

0.77

Answer 2

E = {X is a prime number}

$P ( E ) = P ( 2 ) + P ( 3 ) + P ( 5 ) + P ( 7 ) = 0.62$ , $F = \{ x < 4 \}$

$P ( F ) = P ( 1 ) + P ( 2 ) + P ( 3 ) = 0.50$

and $P ( E \cap F ) = P ( 2 ) + P ( 3 ) = 0.35$

∴ $P ( E \cup F ) = P ( E ) + P ( F ) - P ( E \cap F ) = 0.62 + 0.50 - 0.35 = 0.77$