question_answer 32)

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and it returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a bal is drawn at random. What is the probability that the second ball is red ? 

Answer:

Let R1 = event of drawing a red ball in the first draw.       B2 = event of drawing a red ball in the second draw.       Before first draw, we have total 10 balls [5R and 5B] and before second drawn we have total 12 balls [either 7R and 5B are 7B]       Required probability = P(R1 R2 or B­1 R2)       = P(R1) P) P(R2/R2) + P(B1) P(R2/B1)