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?

1.56% probability that the student gets all three questions right

Step-by-step 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.

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

And p is the probability of X happening.

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

So

Three questions.

This means that

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

This is

1.56% probability that the student gets all three questions right

452,489 to the nearest thousand is 452,000