Ex 13.3, 1

Transcript

Ex 13.3, 1 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? Let B : first ball drawn is black R : second ball is red Probability that the second ball is red = Probability that the first ball is black × Probability that the second ball is red if first is black + Probability that first ball is red × Probability that second ball is red if first is red. P(R) = P(B) . P(R|B) + P(B’) . P(R|B’) Putting above values in (1), P(R) = P(B) . P(R|B) + P(B’) . P(R|B’) = 1﷮2﷯ × 5﷮12﷯ + 1﷮2﷯ × 7﷮12﷯ = 5﷮24﷯ + 7﷮24﷯ = 12﷮24﷯ = 1﷮2﷯ Therefore, Probability that the second ball is red is 𝟏﷮𝟐﷯