Events A and B have probabilities such that P (A) = 0.3, P (B) = 0.25, P (M ∪ N) = 0.425, and P (M ∩ N) = 0.075. Are events A and event B independent? (I think is the middle one)

Question options:

Yes, because P (M) - P (N) = P (M ∩ N)

Yes, because P (M) ∙ P (N) ≠ P (M ∩ N)

Yes, because P (M) ∙ P (N) = P (M ∩ N)

No, because P (M) + P (N) = P (M ∪ N)

No, because P (M) ∙ P (N) ≠ P (M ∪ N)

Question

Velasquez

Mathematics

27 May, 23:27

Events A and B have probabilities such that P (A) = 0.3, P (B) = 0.25, P (M ∪ N) = 0.425, and P (M ∩ N) = 0.075. Are events A and event B independent? (I think is the middle one)

Question options:

Yes, because P (M) - P (N) = P (M ∩ N)

Yes, because P (M) ∙ P (N) ≠ P (M ∩ N)

Yes, because P (M) ∙ P (N) = P (M ∩ N)

No, because P (M) + P (N) = P (M ∪ N)

No, because P (M) ∙ P (N) ≠ P (M ∪ N)

+2

Answers (1)

Know the Answer?

Alfonso Singleton · Answer 1

(C) Yes, because P (M) ∙ P (N) = P (M ∩ N)

Step-by-step explanation:

Two events A and B are independent if P (A) P (B) = P (A ∩ B)

Given events A and B such that:

P (A) = 0.3, P (B) = 0.25, P (A ∪ B) = 0.425, and P (A ∩ B) = 0.075

P (A) P (B) = 0.3 X 0.25 = 0.075 P (A ∩ B) = 0.075

Since the two expression above gives the same answer, they are independent.

The correct option is C.