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A bag contains 5 white, 4 black and 2 red balls. Balls are drawn one by one without replacement. The probability that the 5 t h ball is a red ball, is

Options

  1. A2 11
  2. B4 11
  3. C3 7
  4. D6 11

Correct answer

A. 2 11

Step-by-step solution

If the 5 t h ball is a red ball ⇒ either the first four ball are of other colour and 5 t h ball is red or the first four ball consist of 1 red ball, 3 other ball and 5 t h ball is red ball Hence, the required probability = C 9 4 C 11 4 × 2 7 + C 9 3 × C 2 1 C 11 4 × 1 7 = 9 × 8 × 7 × 6 11 × 10 × 9 × 8 × 2 7 + 9 × 8 × 7 × 2 × 4 11 × 10 × 9 × 8 × 1 7 = 6 55 + 4 55 = 10 55 = 2 11

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