Is there a difference when calculating independent and conditional probabilities?
Example: if A and B are independent, P(AandB)=P(A)*P(B)
but if B is conditional on A : P(AandB|A) = ? I think it's still P(A)*P(B)
2006-07-25 10:10:01 · 4 answers · asked by darcy_t2e 3 in Science & Mathematics ➔ Mathematics
No it is not the same.
By definition, P(X | Y) = P(X & Y) / P(Y). In your case,
P(A & B | A) = P([A & B] & A) / P(A) = P(A & B) / P(B)
The conditional probability P(A & B | A) is 1/P(B) times larger than the unconditional probability P(A & B).
In your case, independence says that
P(A & B) = P(A) . P(B)
so P(A & B | A) = P(A) . P(B) / P(A) = P(B).
2006-07-25 10:20:25 · answer #1 · answered by dutch_prof 4 · 0⤊ 1⤋
I have no idea.....sorry I couldn't help you......But thanks for all that you do to make Yahoo! Answers a better place for everyone
2006-07-25 17:31:40 · answer #2 · answered by suburbsformeandme 1 · 0⤊ 0⤋
Yep. I think you are right.
2006-07-25 17:13:19 · answer #3 · answered by mthtchr05 5 · 0⤊ 0⤋
true
2006-07-25 17:13:02 · answer #4 · answered by Anonymous · 0⤊ 0⤋