Question

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?

Answer 1

`(1/4)^20=1^20/4^20~=1/(1.1xx10^12)=1.1xx10^-12`

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

Explanation:

For each question, there is a probability of `1/4` of guessing the right answer.

One the first question, therefore, we have the probability of `1/4`. If we then guess on the second question, we have another `1/4` chance of getting that right. To see the odds of getting both right, we multiply the two probabilities, and so that's

`1/4 xx 1/4=(1/4)^2=1/16`

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:

`(1/4)^n`, where `n` is the number of questions.

For 20 questions, we have:

`(1/4)^20=1^20/4^20~=1/(1.1xx10^12)=1.1xx10^-12`

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