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 and F = X < 4, find P(E ∪ F).

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

Hint:

Use P(A∪ B)=P(A)+P(B)-P(A∩ B).

Answer 1

The Correct Option is B

Primes in 1,…,8: 2, 3, 5, 7

P(E) = 0.23 + 0.12 + 0.20 + 0.07 = 0.62
P(F) = 0.15 + 0.23 + 0.12 = 0.50
P(E ∩ F) = P(2, 3) = 0.23 + 0.12 = 0.35
P(E ∪ F) = P(E) + P(F) − P(E ∩ F) = 0.62 + 0.50 − 0.35 = 0.77