Question

if P(A) = 0.75 and P(B = 0.8) and P(A' \(\cap\) B') = 0.05 are events A and B independent?

Answer 1

Two events A and B are independent events iff P(A and B) = P(A) x P(B).

Answer 2

hmmm

Answer 3

that's not dependent?

Answer 4

Nope!

Answer 5

In your question, P(not A) = 0.25 and the P(not B) = 0.2 and P(not A and not B) = 0.95.

P(not A) x P(not B) = 0.25 x 0.2 = 0.05 = P(not A and not B)

∴ A and B are independent events.

Answer 6

i thought B was independent if P(A|B) = P(A'|B)

Answer 7

nevermind. i got it

Answer 8

Oh my gosh! There is something majorly wrong with my computer. I was almost finished with the explanation and it froze. I'll start over. Give me a few minutes.

Answer 9

OK good so I don't have to start over. You see that my explanation was right.

Answer 10

yes except for a minor typographical error but understandable

Answer 11

Good! Let me know if you change your mind and want to see the explanation.