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 prime number} and F = {X<4}, the probability of P(EUF) 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∩F) = P(2) + P(3) = 0.35

∴ P(EUF) = P(E) + P(F) – P(E∩F)

= 0.62 + 0.50 – 0.35 = 0.77