A random variable X has the probability distribution : X:  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}, the probability P(E ∪ F) is

0.50 0.77 0.35 0.87

0.77

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(E ∪ F) = P(E)+ P(F)− P(E ∩ F) = 0.62 + 0.50 − 0.35 = 0.77 .