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.

1 Answer
NickTheTurtle
Apr 20, 2017

1152915625≈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 15.

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: 1−45⋅45⋅45⋅45⋅45⋅45=1152915625≈73.79%.

Related questions
See all questions in Basic Probability Concepts
Impact of this question
2053 views around the world
You can reuse this answer
Creative Commons License