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Ex 13.3, 9 - Two groups are competing for position on Board - Ex 13.3

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.3, 9 Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group. Let E : first group wins F : second group wins G : new product is introduced We need to find the Probability that the new product introduced was by the second group i.e. P(F|G) So, P(F|G) = 𝑃 𝐹﷯. 𝑃(𝐺|𝐹)﷮𝑃 𝐸﷯. 𝑃 𝐺|𝐸﷯ + 𝑃 𝐹﷯. 𝑃(𝐺|𝐹)﷯ Putting values in formula, P(F|G) = 0. 4 × 0. 3﷮ 0. 6 × 0. 7 +0. 4 ×0. 3 ﷯ = 0. 12﷮0. 42 + 0. 12﷯ = 0. 12﷮0. 54﷯ = 𝟐﷮𝟗﷯ Therefore, required probability is 𝟐﷮𝟗﷯

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