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 ∪ F) is

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 .