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 wrong?

Answer 1

42.1875% probability that the student gets all three questions wrong

Explanation:

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

Binomial probabily 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.

On a multiple-choice test, each question has 4 possible answers.

One of these options is correct and the other 3 are wrong. We want to find the probability of getting questions wrong. So
`p = (3)/(4) = 0.75`

Three question:

This means that
`n = 3`

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

This is P(X = 3).

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

`P(X = 3) = C_(3,3).(0.75)^(3).(0.25)^(0) = 0.421875`

42.1875% probability that the student gets all three questions wrong