Probability and statistics

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The probability that the life time of randomly chosen device is below average, average,above average are respectively 0.2,0.5,0.3. The probability that of the 3 randomly chosen devices lifetimes of 2 are above average and 1 below average equals

a.0.054,b.0.018,c.0.036,d.0.012

  • Probability and statistics -

    Think of the expansion of the polynomial
    (A+B+C)^3 where A=below, B=averave, C=above, and A+B+C=1.

    1 is below average = A (0.2)
    2 are above average = C (0.3)
    term=AC^2

    The coefficient of AC^2 is 3, i.e. 3AC^2.

    The probability is therefore
    3*0.2*0.3^2=0.054

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