Question
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
Solution
Number of red balls = 5
Number of black balls = 5
∴ total number of balls = 10
Let A be the event that second drawn ball is red, and B be the event of drawing first ball as red and adding two red balls to urn.
Required probability = P(A)= P(B) P(A | B) + P(B') P(A | B')
= P (a red ball is drawn and returned along with 2 red balls and then a red ball is drawn) + P(a black ball is drawn and returned along with 2 black balls and then a red ball is drawn)
