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?

Question

3500 views around the world

You can reuse this answer
Creative Commons License

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%#.