When answering a question on a multiple choice exam, Jon either thinks he knows the answer...

When answering a question on a multiple choice exam, Jon either thinks he knows the answer or just guesses.

Suppose the probability that Jon thinks he knows the answer is 0.75 and there’s a 90% chance that he’ll get the question correct if he thinks he knows the answer. There are 5 choices for each multiple-choice exam question.

Each question is worth 2 marks (no part marks), but blank answers earn 0.4 marks. Suppose Jon always answers the question if he thinks he knows the answer, but if he does not, he guesses the answer (at random) half the time and the other half of the time, he leaves the answer blank.

What is the expected value of Jon’s score on a randomly selected question?

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milcah answered 8 months ago

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