SOLUTION: A quiz has 4 multiple choice questions and each has 5 choices. What is the probability of getting at least 2 answers right by guessing?
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Question 1117792: A quiz has 4 multiple choice questions and each has 5 choices. What is the probability of getting at least 2 answers right by guessing? Answer by ikleyn(52816) (Show Source):
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The method to solve this problem is to consider the probability of the complement set of events.
The complement set of events is (to give exactly one correct answer when answering to all four multiple choice questions) ,
or (to give all incorrect answers).
Again: the complement set of events is (to give the correct answer to exactly one of the four multiply choice and to give incorrect
answers to the three other questions) or (to give incorrect answers to all 4 multiply choice questions).
Since each of 4 multiple choice question has 5 choices, the probability to randomly guess the answer correctly
to each of the questions is .
Correspondingly, the probability to give randomly incorrect answer to EACH SEPARATE of the four questions is .
Therefore, the probability to give randomly correct answer to any one fixed question and to give incorrect answer
to all of remaining three questions is .
It means that with four multiply choice questions, to give the correct answer to one of the four multiply choice and to give incorrect
answer to the three other questions is four time of that, i.e.
= (*)
Very good. Now, the probability to give all 4 incorrect answers to all 4 questions is . (**)
Then the final probability under the question is the complement to the sum of (*) and (**):
1 - - = 0.1808 = 18.08%.
