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    Question

    A box contains 6 red, 4 blue, 2 green and 4 yellow hats.

    Two hats are picked at random, what is the probability

    that all hats are of green colour?
    A 1/150 Correct Answer Incorrect Answer
    B 22/145 Correct Answer Incorrect Answer
    C 9/115 Correct Answer Incorrect Answer
    D 3/116 Correct Answer Incorrect Answer
    E 1/120 Correct Answer Incorrect Answer

    Solution

    Total number of hats = 6 + 4 + 2 + 4 = 16 Let S be the sample space. Then, n(S) = number of ways of drawing 2 hats out of 16 = ¹⁶C_₂ = (16 × 15)/( 2 × 1) = 120 Let E= event of drawing all the hats are of green colour n(E) = ²C_₂ = 1 ∴ P (E) = (n(E))/(n(S)) = 1/120

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