Question

On a multiple-choice test, each question has 4 possible answers. A student does not know

answers to three questions, so the student guesses.
What is the probability that the student gets all three questions right?

Answer 1

1.56% probability that the student gets all three questions right

Explanation:

For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

Each question has 4 possible answers, one of which is correct.

So
`p = \frac{1}[4} = 0.25`

Three questions.

This means that
`n = 3`

What is the probability that the student gets all three questions right?

This is
`P(X = 3)`

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 3) = C_(3,3).(0.25)^(3).(0.75)^(0) = 0.0156`

1.56% probability that the student gets all three questions right