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
Answer & explanation
Correct answer: option 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(E ∪ F) = P(E)+ P(F)− P(E ∩ F) = 0.62 + 0.50 − 0.35 = 0.77 .