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99 Percentile Qs Bank for JEE MainMathematicsProbability

A bag contains 12 red balls and 6 white balls. Six balls are drawn one by one without replacement of which at least 4 balls are white. Find the probability that in the next two drawns exactly one white ball is drawn. (Leave answer in n C r ).

Options

  1. A1 2 C 2 · 6 C 4 1 8 C 6 · 1 0 C 1 · 2 C 1 1 2 C 2 + 1 2 C 1 · 6 C 5 1 8 C 6 &middo
  2. B1 2 C 2 · 6 C 4 1 8 C 6 · 1 0 C 1 · 2 C 1 1 2 C 2 - 1 2 C 1 · 6 C 5 1 8 C 6 &middo
  3. C1 2 C 2 · 6 C 4 · 1 0 C 1 2 C 1 1 2 C 2 2 + 1 2 C 1 · 6 C 1 · 1 1 C 1 · 1 1
  4. D1 2 C 2 · 6 C 4 · 1 0 C 1 1 2 C 2 2 - 1 2 C 1 · 6 C 1 · 1 1 C 1 1 2 C 2 2

Correct answer

A. 1 2 C 2 · 6 C 4 1 8 C 6 · 1 0 C 1 · 2 C 1 1 2 C 2 + 1 2 C 1 · 6 C 5 1 8 C 6 &middo

Step-by-step solution

Let A 1 be the event exactly 4 white balls have been drawn. A 2 be the event exactly 5 white balls have been drawn. A 3 be the event exactly 1 white ball is drawn from two draws. Then, P B = P B A 1 P A 1 + P B A 2 P A 2 + P B A 3 P A 3 But P B A 3 = 0 ∵ there are only 6 white balls in the bag ∴ P B = P B A 1 P A 1 + P B A 2 P A 2 = 1 2 C 2 · 6 C 4 1 8 C 6 · 1 0 C 1 · 2 C 1 1 2 C 2 + 1 2 C 1 · 6 C 5 1 8 C 6 · 1 1 C 1 · 1 C 1 1 2 C 2

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