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Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.)
(a) What is the probability that he will answer all questions correctly?

Submitted: 11 months ago.Category: Calculus and Above
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9/22/2017
Tutor: Ryan, Engineer replied 11 months ago
Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 9,184
Experience: B.S. in Civil Engineering
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Hi,

Thank you for using the site. I'll be happy to help you with this problem.

Since each question has five answers, the probability of guessing the correct answer for ONE question is 1/5, or 0.20.

The probability that he can guess all four answers correctly is then 0.2 * 0.2 * 0.2 * 0.2 = 0.0016

Thanks,

Ryan

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Tutor: Ryan, Engineer replied 11 months ago

Oh...rounded to three decimal places, the probability is 0.002.

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