# 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 correctly?

##### 1 Answer

We can therefore say, very roughly, that the probability is slightly over one trillionth.

#### Explanation:

For each question, there is a probability of

One the first question, therefore, we have the probability of

We can generalize and say that for any number of questions where we are guessing among 4 answers each time, the probability of getting them all right is:

For 20 questions, we have:

We can therefore say, very roughly, that the probability is slightly over one trillionth.