Dear Forum I am having trouble with the following word problem any help would be appreciated , thank you ,
An urn contains 4 red and 5 white balls. Two balls are drawn out in succession without replacement. If the second ball is white, what is the probability that the first ball was white?
B = event that the second ball is white
Originally Posted by AlgebraicallyChallenged
A = event that the first ball is white
P(A given B) = P (A | B) = P(A and B) divided by P(B).
P(A and B) = (5/9) (4/8) = 20/72 = 5/18
P(B) is the sum of the two outcomes:
Outcome 1: First ball is white, Second ball is white P= 5/18
Outcome 2: First ball is not white, second ball is white P = (4/9) (5/8) = 5/18
So P(B) = 5/18 + 5/18 = 10/18 = 5/9
Then P(A|B) = (5/18) divided by (5/9) which gives 1/2.
So there is a 50% chance that, given that the second ball is white, the first ball is white as well.
Notice that that is exactly the same answer as if the question had been "Given that the first ball is white, what is the probability that the second is also white".