
You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. You gain 1 point when you answer a question correctly and 0 points when you answer a question incorrectly. What is the expected value of the quiz?

For each question, you have a 25% probability of guessing the correct answer. So, your expected value for the 10 questions is
In other words, if you consistently applied this testtaking strategy, over the long run, you should expect your test score average to be 2.5 points.
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. You gain 1 point when you answer a question correctly and lose ¼ point when you answer a question incorrectly. What is the expected value of the quiz?
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer every question incorrectly?

The probability that you answer every question incorrectly is
So, with this testtaking strategy, you have about a 6% chance of answering every question incorrectly.
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer every question correctly?
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer only the first question correctly?

The probability that you answer only the first question correctly is
So, with this testtaking strategy, you have about a 2% chance of answering only the first question correctly.
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer only the first five questions correctly?
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You take a 10question multiplechoice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer at least one question correctly?

The probability that you answer every question incorrectly is
So, the probability that you answer at least one quesiton correctly is
So, with this testtaking strategy, you have about a 94% chance of answering at least one question correctly.
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