# Example 16 - Chapter 13 Class 12 Probability (Term 2)

Last updated at May 29, 2018 by Teachoo

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Chapter 13 Class 12 Probability (Term 2)

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Example 16 Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II. Let E1 : Bag selected is bag 1 E2 : Bag selected is bag 2 A : Ball selected is Red B : Ball selected is Black We need to find P(ball was drawn from bag 2, if ball is red) = P(E2|A) We need to find, 𝑃 𝐸2|𝐴= 𝑃 𝐴 𝑃(𝐴|𝐸2)𝑃 𝐸1 𝑃 𝐴|𝐸1 + 𝑃 𝐸2 𝑃(𝐴|𝐸2) Putting values in formula, P(E2|A) = 12 × 511 12 × 37 + 12 × 511 = 12 × 511 12 [ 37 × 511 ] = 511 33 + 3577 = 511 6877 = 511 × 7768 = 3568 Therefore, required probability is 𝟑𝟓𝟔𝟖