Ex 13.3, 2

Transcript

Ex 13.3, 2 A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag. Let B1 : ball is drawn from Bag I B2 : ball is drawn from Bag II R : ball is drawn is red We need to find Now, Probability that ball is drawn from Bag I, if ball is red = P(B1 |R) So, P(B1 |R) = P 𝐵﷮1﷯﷯ . P(𝑅| 𝐵﷮1﷯)﷮P 𝐵﷮1﷯﷯ . P(𝑅| 𝐵﷮1﷯)+P 𝐵﷮2﷯﷯ . P(𝑅| 𝐵﷮2﷯)﷯ Putting values in formula, P(B1 |R) = 1﷮2﷯ × 1﷮2﷯﷮ 1﷮2﷯ × 1﷮4﷯ + 1﷮2﷯ × 1﷮2﷯﷯ = 1﷮4﷯ ﷮ 1﷮8﷯ + 1﷮4﷯ ﷯ = 2﷮8﷯ ﷮ 3﷮8﷯ ﷯ = 2﷮3﷯ Therefore, required probability is 𝟐﷮𝟑﷯