PROBABLITY QUESTION

Question

An urn contains 55 red and 66

white balls. Two balls are drawn in succession without replacement. If the second ball is​ white, what is the probability that the first ball was​white?

Answer 1

This shows application of Bayes Theorem.

P(2nd Ball is white) = P(WW) + P(RW) = (1/66)(1/65) + (1/55)(1/66)

P(1stball is white and 2nd ball is white ) = (1/66)(1/65)

P(1st ball is white| 2nd ball is white) = (1/66)(1/65) / (1/66)(1/65) + (1/55)(1/66) ] = (1/65) / [(1/65)+(1/55)]

= 55/(65+55) = 11/24