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.

Apr 20, 2017

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 $\frac{1}{5}$.

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 $1 - P \left(\text{all remaining 6 questions wrong}\right)$.

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%.