SOLUTION: A student who has not studied for a multiple-choice test decides to guess the answers for every question. There are three questions, and three choices of answer (A, B and C) for

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Question 1195726: A student who has not studied for a multiple-choice test decides to guess the answers for every
question. There are three questions, and three choices of answer (A, B and C) for each question. Given
that only one of the possible choices (A, B or C) is correct for each question, state the probability that
the student guesses:
a 1 correct answer b 2 correct answers c 3 correct answers d 0 correct answer
Answer by math_helper(2461) About Me  (Show Source):
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There are 3*3*3 = 27 possible outcomes



# correct   Formulation              Probability      Notes

   0        (2/3)*(2/3)*(2/3)            8/27       

   1        3C1*(1/3)*(2/3)*(2/3)       12/27         3C1 = 3!/(2!*1!) = 3

   2        3C2*(1/3)*(1/3)*(2/3)        6/27         3C2 = 3!/(1!*2!) = 3 

   3        (1/3)*(1/3)*(1/3)            1/27