Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. If one ball is drawn at random from one of the bags and is found to be red, then the probability that it was drawn from the bag B is

Step-by-step solution

E₁ ~A ball is drawn from bag AE₂ ~A ball is drawn from bag BF A ball is found to be red aligned & P (E₁ )= 1 2 , P (E₂ )= 1 2 , P ( F E₁ )= 3 5 , P ( F E₂ )= 5 9 & P ( E₂ F )= P ( F E₂ ) P (E₂ ) P ( F E₁ ) P (E₁ )+P ( F E₂ ) P (E₂ ) & = 5 9 1 2 3 5 1 2 + 5 9 1 2 = 5 9 3 5 + 5 9 = 25 52 . aligned