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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

Options

  1. A1 2
  2. B3 4
  3. C4 5
  4. D5 11

Correct answer

B. 3 4

Step-by-step solution

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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