Suppose that you take a 20 question multiple-choice quiz by guessing. Each question has exactly one correct answer of the four alternatives given. What is the probability of getting all 20 questions incorrectly?

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Answer 1 · 2017-07-18T01:26:10

All wrong: #(3/4)^20~=.0032=0.32%#.

All right:
#(1/4)^20~=9.1xx10^(-13)=0.00000000000091%#.

For each question, there are 3 incorrect answers and 1 correct answer. Each question is a separate event and so we multiply the probabilities.

All answers wrong

That's #3/4xx3/4xx3/4xx...3/4# twenty times, so we can express it as:

#(3/4)^20~=.0032=0.32%#.

All answers right

#(1/4)^20~=9.1xx10^(-13)=0.00000000000091%#.