A box contains 1 black and 1 white ball. A ball is drawn randomly and replaced in the box with an additional ball of the same colour, then a second ball is drawn randomly from the box containing 3 balls. The probability that the first drawn ball was white given that at least one of the two balls drawn was white is

Question

A box contains 1 black and 1 white ball. A ball is drawn randomly and replaced in the box with an additional ball of the same colour, then a second ball is drawn randomly from the box containing 3 balls. The probability that the first drawn ball was white given that at least one of the two balls drawn was white is, 1 2, 3 4, 4 5, 5 11

MARKS App · Accepted Answer

B → first ball drawn is white A → At least one of two balls drawn are white P A = W W + W B + B W = 1 2 × 2 3 + 1 2 × 1 3 + 1 2 × 1 3 = 4 6 = 2 3 = P B A = P B ∩ A P A = 1 2 × 2 3 + 1 2 × 1 3 2 3 = 1 2 2 3 = 3 4

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