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    Question

    In a Bag, there are 20 Hairbands

    of three different colours; red, blue, and black. The probability of picking 2 red Hairbands at random without replacement is (1/19) , and the probability of picking 2 blue Hairbands at random without replacement is (14/95). Suppose the number of black colour Hairbands in the box is 'p', then determine which of the following quadratic equation has roots that are (p + 2) and (p - 2) respectively. 
    A q² - 14q + 45 Correct Answer Incorrect Answer
    B q² - 18q - 75 Correct Answer Incorrect Answer
    C q² + 10q - 45 Correct Answer Incorrect Answer
    D q² + 12q - 112 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the number of red and blue hairbands be 'r' and 'b' respectively, r + b + p = 20 ATQ; (rC2/20C2) = (1/19) {r(r - 1) /2} = 190 × (1/19) r(r - 1) = 20 'r' = 5 Again, (bC2/20C2) = (14/95) b(b - 1) /2 = 190 × (14/95) b(b - 1) = 56 'b' = 8 So, = 20 - 8 - 5 'p' = 7 Required roots: (p + 2) = 9 and (p - 2) = 5 So, required quadratic equation = (q - 9) (q - 5) = q² - 14q + 45

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