If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?

Question

Mathematics

Tiffany Schmitt

16 July, 11:50

If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?

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Uriel Coffey · Answer 1

There is a 1/5 chance of getting each question correct. The probability of getting at least 1 correct is written as such:

P (X ≥ 1) = 1 - P (X = 0)

This is because the only other option than getting at least one correct is to get nothing correct.

Since there is a 1/5 chance of getting each question correct, there is a 4/5 chance of getting each question wrong:

1 - P (X = 0) = 1 - (4/5) ^10 (since there are 10 questions, with a 4/5 chance of missing each one)

= 1 - 0.1073741824 ≈ 0.8926 = 89.26% chance of getting at least one question correct. Given this probability, it is reasonable to expect to pass by guessing.