Consider two events such that P (A) = 3/4, P (B) = 2/5 and P (AnB) = 1/3. Are the events A and B independent?

Yes, they are independent because P (A) xP (B) = P (AnB)

No, they are dependent because P (A) xP (B) = P (AnB)

Yes they are independent because P (A) xP (B) doesn't equal

P (AnB)

No, they are dependent because P (A) xP (B) doesn't equal P (AnB)

Question

Mathematics

Kaleb

2 June, 09:21

Consider two events such that P (A) = 3/4, P (B) = 2/5 and P (AnB) = 1/3. Are the events A and B independent?

Yes, they are independent because P (A) xP (B) = P (AnB)

No, they are dependent because P (A) xP (B) = P (AnB)

Yes they are independent because P (A) xP (B) doesn't equal

P (AnB)

No, they are dependent because P (A) xP (B) doesn't equal P (AnB)

+2

Answers (1)

Know the Answer?

Judd · Answer 1

If P (A) times P (B) is equal to P (A n B), then that shows the events are independent. Otherwise, they are dependent. When I write "A n B", I mean "A intersect B". The intersect symbol looks similar to the lowercase letter n.

P (A) * P (B) = (3/4) * (2/5) = (3*2) / (4*5) = 6/20 = 3/10

Since that result is not the same as P (A n B) = 1/3, this means that the events are not independent. They are dependent events. The answer is choice D