P(A) = 0.27, P(B) = 0.40, and P(A∩B) = 0.108. Are events A and B independent? Justify the answer mathematically.

Yes, because 0.27 + 0.40 ≠ 0.108
No, because 0.27 + 0.40 ≠ 0.108
Yes, because (0.27)(0.40) = 0.108
No, because (0.27)(0.40) = 0.108

Question

P(A) = 0.27, P(B) = 0.40, and P(A∩B) = 0.108. Are events A and B independent? Justify the answer mathematically.

Yes, because 0.27 + 0.40 ≠ 0.108
 No, because 0.27 + 0.40 ≠ 0.108
 Yes, because (0.27)(0.40) = 0.108
 No, because (0.27)(0.40) = 0.108

toga · Answer

The correct answer is d) No, because (0.27)(0.40) = 0.108.

Two events A and B are considered independent if and only if the probability of their intersection (A ∩ B) is equal to the product of their individual probabilities (P(A) × P(B)).

In this case, P(A) = 0.27, P(B) = 0.40, and P(A ∩ B) = 0.108.

So, P(A) × P(B) = (0.27)(0.40) = 0.108.

Since P(A ∩ B) = 0.108, which is equal to P(A) × P(B), events A and B are not independent. Therefore, the correct answer is d) No, because (0.27)(0.40) = 0.108.