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    Question

    Bag A contains 11 colour pencils and 19 normal pencils.

    Bag B contains 15 colour 4 pencils and 20 normal pencils. A bag is selected at random, and a pencil is drawn from it. It turns out to be a colour pencil. What is the probability that it came from Bag A?
    A 80/167 Correct Answer Incorrect Answer
    B 79/167 Correct Answer Incorrect Answer
    C 77/167 Correct Answer Incorrect Answer
    D 59/162 Correct Answer Incorrect Answer

    Solution

    Probability of selecting Bag A = 1/2 Probability of selecting Bag B = 1/2 Bag A:
    Total pencils = 11 + 19 = 30 P (colour/A) = 11/30 Bag B:
    Total pencils = 15 + 20 = 35 P (colour/B) = 15/35 = 3/7 Total probability of getting a colour pencil P (C) = (1/2) x (11/30) + (1/2) x (3/7) P (C) = 167/420 Required probability = {(1/2) x (11/30)}/ 167/420 = 77/167

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