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A box contains x red balls and 10 black balls. 3 balls are drawn one by one without replacement. If the probability of choosing 3 red balls is equal to the probability of choosing 2 red and 1 black ball, then the possible value of x can be

Options

  1. A1
  2. B32
  3. C53
  4. D40

Correct answer

B. 32

Step-by-step solution

Probability of choosing 3 red balls = x C 3 10 + x C 3 Probability of choosing 2 red balls and one black ball = x C 2   10 C 1 10 + x C 3 So, x C 3 10 + x C 3 = x C 2   10 C 1 10 + x C 3 ⇒ x C 3 = x C 2   10 C 1 ⇒ x C 3 x C 2 = 10 ⇒ x - 3 + 1 3 = 10 ⇒ x = 3 2

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