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March 30, 2017

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The probability that a voting-age adult in 2004 voted in the presidential election was 0.57. Five voting-age adults in 2004 were randomly selected. Find the probability that exactly 2 or the 5 adults voted in the presidential election.

  • MATH - ,

    prob(voting) = .57
    prob(not voting) = .43

    prob(2 of 5 voted)
    = C(5,2) (.57)^2 (.43)^3
    = .2583

  • MATH - ,

    p=probability of voting
    q=(1-p)=probability of not voting.

    Out of 5 adults randomly selected, the probability that exactly 2 voted is calculated according to the binomial expansion,
    C(5,2)p^2q^3
    =(5!/(2!3!))*0.57^2*0.43^3
    =0.258 (approx.)

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