Consider two events E1 and E2 such that P(E1) = 1/2, P(E2) = 1/3, and P(E1 intersect E2) = 1/5. Which of the following s...

Question

Consider two events E1 and E2 such that P(E1) = 1/2, P(E2) = 1/3, and P(E1 intersect E2) = 1/5. Which of the following statements is/are true?

A. P(E1 union E2) = 19/30
B. Events E1 and E2 are independent
C. Events E1 and E2 are not independent
D. P(E1 | E2) = 4/5

Accepted Answer

C. Events E1 and E2 are not independent Two events are given with their individual probabilities and the probability of their intersection. Independence requires P(E1 intersect E2) = P(E1)*P(E2). We check this condition and evaluate each statement.

Consider two events E1 and E2 such that P(E1) = 1/2, P(E2) = 1/3, and P(E1 intersect E2) = 1/5. Which of the following statements is/are true? A. P(E1 union E2) = 19/30 B. Events E1 and E2 are independent C. Events E1 and E2 are not independent D. P(E1 | E2) = 4/5