Question

A student is certain of the answers to 4 questions but is totally baffled by 6 questions. If the student randomly guesses the answers to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? E

The multiple choice test has 10 questions and each question has 5 possible answers.

Answer 1

`11529/15625~~73.79%`

Explanation:

Let us assume that the student gets the `4` questions which he is certain of correctly.

Now, he randomly guesses the remaining `6` questions, which each have `5` options. The probability of him getting a particular problem correctly is `1/5`.

In order to score a `5` or more, he needs to get at least `1` of the remaining `6` questions correctly. We can find the probability that he gets exactly `1` question correct, `2` questions correct, `3` questions correct, …, and `6` questions correct. Adding these probabilities will give us the correct answer.

But there is an easier way. We can calculate the probability that he will not get a score of `5` or more and subtract it from `1`. In other words, we calculate `1-P("all remaining 6 questions wrong")`.

Assuming that answering the remaining six questions are independent events, we can just multiply the probabilities of getting one question wrong: `1-4/5*4/5*4/5*4/5*4/5*4/5=11529/15625~~73.79%`.