# 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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