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Paragraph: Let U₁ and U₂ be two urns such that U₁ contains 3 white and 2 red balls and U₂ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U₁ and put into U₂ . However, if tail appears then 2 balls are drawn at random from U₁ and put into U₂ . Now, 1 ball is drawn at random from U₂ . Question: Given that the drawn ball from U₂ is white, the probability that head a

Options

  1. A17 23
  2. B11 23
  3. C15 23
  4. D12 23

Correct answer

D. 12 23

Step-by-step solution

P (head appeared/white from V₂ ) aligned & =P(H) ^3 C₁ ^5 C₁ ^2 C₁ ^2 C₁ + ^2 C₁ ^5 C₁ ^1 C₁ ^2 C₁ 23 30 & = 1 2 3 5 1+ 2 5 1 2 23 30 = 12 23 & aligned

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