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A box ' A ' contanis 2 white, 3 red and 2 black balls. Another box ' B^ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' B^ is

Options

  1. A7 16
  2. B9 32
  3. C7 8
  4. D9 16

Correct answer

A. 7 16

Step-by-step solution

Probability of drawing a white ball and then a red ball from bag B is given by ^4 C₁ ^2 C₁ ^9 C₂ = 2 9 Probability of drawing a white ball and then a red ball from bag A is given by ^2 C₁ ^3 C₁ ^7 C₂ = 2 7 Hence, the probability of drawing a white ball and then a red ball from bag B = 2 9 2 7 + 2 9 = 2 7 18+14 = 7 16

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