SOLUTION: A multiple-choice test has 6 questions. Each question has 5 choices and only one of which is correct. If a student guesses the answer for each question find the probability that t

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Question 1137149: A multiple-choice test has 6 questions. Each question has 5 choices and only one of which is correct. If a
student guesses the answer for each question find the probability that the students gets exactly 3 questions correct

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The probability to guess randomly the correct answer for each question is  1%2F6.


The probability to guess correctly 3 fixed questions of 5 is  1%2F6%5E3.


But there are  C%5B5%5D%5E3 = %285%2A4%29%2F%281%2A2%29 = 10  ways to select these 3 questions among the given 5.


So, the final probability is  P = 10%2F6%5E3 = 0.04627 = 4.627%.