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    Question

    Three boxes B1, B2, B3 contain red and green balls in

    the ratio 1:1, 3:5, and 5:3 respectively. A box is selected at random and a ball is drawn. What is the probability that the selected ball is red?
    A 1/4 Correct Answer Incorrect Answer
    B 1/8 Correct Answer Incorrect Answer
    C 1/16 Correct Answer Incorrect Answer
    D 1/2 Correct Answer Incorrect Answer

    Solution

    We are given:

    • Three boxes: B1, B2, B3
    • Each is equally likely to be chosen ⇒ P(B1) = P(B2) = P(B3) = 1/3
    • Ball is drawn from the selected box
    • Ratios of red to green balls:
      • B1: 1 : 1 ⇒ Red = 1/2
      • B2: 3 : 5 ⇒ Red = 3 / (3 + 5) = 3/8
      • B3: 5 : 3 ⇒ Red = 5 / (5 + 3) = 5/8
    Using Total Probability Theorem Let R be the event "red ball is drawn" Then: P(R) = P(B1)·P(R|B1) + P(B2)·P(R|B2) + P(B3)·P(R|B3)
    = (1/3)·(1/2) + (1/3)·(3/8) + (1/3)·(5/8)
    = (1/6) + (1/8) + (5/24) Now take LCM = 24:
    • (1/6) = 4/24
    • (1/8) = 3/24
    • (5/24) = 5/24
    Add: 4/24 + 3/24 + 5/24 = 12/24 = 1/2

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