# 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?

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

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

#### Explanation:

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

That's $\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} \times \ldots \frac{3}{4}$ twenty times, so we can express it as:
(3/4)^20~=.0032=0.32%.
(1/4)^20~=9.1xx10^(-13)=0.00000000000091%.