Question

What is the value of the conditional probability P(A∩B | B)?

Answer 1

It seems to me that \[P[(A\cap B)/ B] = P(A/B).\] Is this correct?

Answer 2

yep

Answer 3

OK. My reference says that it equals 1, because it is a certain event. But this doesn't seem to make any sense. Could you confirm or deny it?

Answer 4

I agree!

Answer 5

Do you agree with my original answer, Chlorophyll?

Answer 6

Yep!

Answer 7

what reference?

Answer 8

Should you post specific problem to prove it!

Answer 9

\[P(A|B)=\frac{P(A\cap B)}{P(B)}\] and so replacing A by \(A\cap B\) you get
\[P(A\cap B|B)=\frac{P(A \cap B \cap B)}{P(B)}\] but if i am not mistaken \(A\cap B\cap B=A\cap B\)

Answer 10

satellite73: Yes, this is what I thought. The reference I referred to are lecture notes. The specific situation is p(A) = 1/2; p(B) = 1/3 and p(A∩B)=1/4.