statistics

A multiple choice test has 3 questions and each question has 3 choices. If Nacho takes this test, what is the probability that he will: (a)answer all questions correctly? (b)answer all questions wrong? (c)answer two questions correctly?

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  1. W - wrong
    R - right

    a) prob RRR = (1/3)(1/3)(1/3) = 1/27
    b) prob WWW = (2/3)^3 = 8/27
    c) 2 right could be
    WRR, RWR, or RRW
    prob(of that) = 3 x (2/3)(1/3)^2 = 6/27

    (notice the other case is 2 wrong
    prob of that = 3(1/3)(2/3)^2 = 12/27

    and notice that 1/27 + 8/27 + 6/27 + 12/27 = 27/27 as it should be

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