A particular multiple choice test has 110 questions, each with four choices (only one of which is correct).

If students were to take the test by guessing the answer to every question on it entirely at random, what would you expect the average number of correct responses per test to be? Provide your response precise to the nearest tenth.

My answer is only an approximation, but because the number of questions is large (110) and the required precision low (0.1), it should be good enough:

There are 4 answers per question, so the probability of guessing correctly is 0.25. 0.25*110 = 27.5

The answer based on our approximation is 27.5. Otherwise there is a well studied probability distribution that governs this problem - one could use it to get a more accurate answer.

Mar 14th, 2015

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