Probability of Getting 40/40 on MCQ Test by Guessing

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SUMMARY

The probability of achieving a perfect score of 40/40 on a multiple-choice question (MCQ) test with 40 questions, each having 4 possible answers, is calculated as (1/4)^40. This formula accurately reflects the scenario of guessing each answer. The alternative approach using combinations, specifically 1/(160C40), is incorrect as it implies selecting multiple answers for a single question. Additionally, if a student is confident about 30 questions and must guess on 10, the probability of scoring above 30 is contingent on not missing all guessed questions.

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Homework Statement



This question isn't in a book, but I want to know the answer for myself.

Q. If I take an MCQ test with 40 questions, each question has 4 possible answers with only one being correct, what is the probability of getting 40/40 in the test by guessing?

I've tried solving this by doing (1/4)^40, but then I thought of doing 1/(160C40) and I got different answers. Why is that so and which is the correct way.

Q. If I am sure of 30 questions and unsure about 10 (have to guess them), what is the probability of getting above 30 in the test.(I don't lose marks for wrong answers)
 
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mohdakram said:

Homework Statement



This question isn't in a book, but I want to know the answer for myself.

Q. If I take an MCQ test with 40 questions, each question has 4 possible answers with only one being correct, what is the probability of getting 40/40 in the test by guessing?

I've tried solving this by doing (1/4)^40, but then I thought of doing 1/(160C40) and I got different answers. Why is that so and which is the correct way.

Q. If I am sure of 30 questions and unsure about 10 (have to guess them), what is the probability of getting above 30 in the test.(I don't lose marks for wrong answers)
For the first question, (1/4)^40 is correct. Your other answer involving C(160,40) seems to assume you can select more than one answer to a single question.

For the second question, your score will be above 30 unless you miss all 10 questions you guess at. What's the probability of that?
 
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