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      Question

      There are twelve boxes out of which only four boxes

      contain chocolates, and remaining boxes are empty. You picked one of the boxes randomly. Now the owner of boxes opened four more boxes, out of which one box contains chocolates and the other three are empty. The owner now gives you the opportunity to switch the already picked box. If you switched the box randomly, then find the probability that the box you picked now contains chocolates. (Note: Owner already knows the boxes which contain chocolates)
      A 3/7 Correct Answer Incorrect Answer
      B 2/7 Correct Answer Incorrect Answer
      C 1/3 Correct Answer Incorrect Answer
      D 4/7 Correct Answer Incorrect Answer
      E 8/21 Correct Answer Incorrect Answer

      Solution

      Probability that the box picked by you initially contains chocolates = (4/12) = (1/3) Probability that the box picked by you initially does not contain chocolates = 1 - (1/3) = (2/3) Remaining number of boxes = 12 - 4 - 1 = 7 Case I: when the box picked by you contains chocolates Out of the remaining 7 boxes, two contain chocolates Probability that the box picked by you now contains chocolates = (2/7) Case II: when the box picked by you does not contain chocolates Out of the remaining 7 boxes, three contain chocolates Probability that the box picked by you now contains chocolates = (3/7) Required probability = (1/3) X (2/7) + (2/3) X (3/7) = (2/21) + (6/21) = (8/21)

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