Urn A contains 3 white and 4 black balls, while Urn B contains 2 white and 3 black balls. Two balls are randomly transferred from Urn A to Urn B simultaneously. Subsequently, a single ball is drawn from Urn B and is found to be black. The probability that the two balls transferred were of different colours is

Step-by-step solution

Let the events for the transferred balls be: E₁ : 2 white balls are transferred E₂ : 1 white and 1 black ball are transferred E₃ : 2 black balls are transferred The probabilities of these transfers from Urn A are: P(E₁) = ³C₂ ⁷C₂ = 3 21 = 1 7 P(E₂) = ³C₁ ⁴C₁ ⁷C₂ = 12 21 = 4 7 P(E₃) = ⁴C₂ ⁷C₂ = 6 21 = 2 7 Let B be the event that the ball drawn from Urn B is black. The new composition of Urn B (originally 2 white, 3 black) in each case is: For E₁ : 4 white, 3 black P(B|E₁) = 3 7 For E₂ : 3 white, 4 black P(B|E₂) = 4