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Probability

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Darby guesses the answers to six questions on the math portion of her college entrance exam. Each question is a true or false question. What is the approximate probability that at least 4 of her answers are correct?

A. 0.23
B. 0.34
C. 0.66
D. 0.78

  • Probability -

    P(at least 4 correct)
    = P(4 correct) + P(5 correct) + P(6 correct)
    = 6C4 (½)^4 (½)^2 + 6C5 (½)^5 (½)^1 + 6C6 (½)^6 (½)^0
    ... four correct answers, two incorrect, in any order plus five correct answers, one incorrect, in any order, plus six correct answers, zero incorrect, and only one possible order ...
    = 15 (½)^6 + 6 (½)^6 + 1 (½)^6
    = (15+6+1) / (2^6)
    = 22 / 64
    = 11 / 32
    = 0.34375

  • Probability -

    How did you get this?
    = 6C4 (½)^4 (½)^2 + 6C5 (½)^5 (½)^1 + 6C6 (½)^6 (½)^0

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