# Ex 13.3, 9 - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Chapter 13 Class 12 Probability

Serial order wise

Last updated at April 16, 2024 by Teachoo

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) P(F|G) = (𝑃(𝐹). 𝑃(𝐺"|" 𝐹))/(𝑃(𝐸). 𝑃(𝐺"|" 𝐸) + 𝑃(𝐹). 𝑃(𝐺"|" 𝐹)) "P(E)" = Probability that first group wins = 𝟎.𝟔 "P(G|E)" = Probability that new product is introduced, if first group wins = 0.7 "P(F)" = Probability that the second group wins = 0.4 "P(G|F)" = Probability that the a new product is introduced, if second group wins = 𝟎.𝟑 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