Question

Considering that the probability of event C is 0.44, the probability of event D is 0.20, and the probability of their intersection is 0.088, determine whether C and D are dependent or independent events.

Answer 1

Events C and D are independent.

Step-by-step explanation:

Events C and D are dependent. To determine if events C and D are independent or dependent, we need to compare the probability of their intersection, P(C ∩ D), with the product of their individual probabilities, P(C) and P(D).

If events C and D are independent, then P(C ∩ D) = P(C) × P(D). However, if P(C ∩ D) ≠ P(C) × P(D), then events C and D are dependent.

In this case, we have P(C) = 0.44, P(D) = 0.20, and P(C ∩ D) = 0.088. Calculating the product of their probabilities, we get P(C) × P(D) = 0.44 × 0.20 = 0.088.

Since P(C ∩ D) = P(C) × P(D), we can conclude that events C and D are independent.