College

A student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question.

Find the probability of guessing at least 15 out of 20 correctly. Would you consider this event likely or unlikely to occur? Explain your answer.

Answer :

Final answer:

The probability of guessing at least 15 out of 20 questions correctly on a multiple-choice exam can be calculated using the binomial probability formula. It is very unlikely to occur due to the low probability of randomly guessing the correct answers on a multiple-choice exam.


Explanation:

When guessing on a multiple-choice exam with five choices for each question, the probability of guessing a single question correctly is 1/5 or 0.2. To find the probability of guessing at least 15 out of 20 correctly, we can use the binomial probability formula. The probability of guessing exactly k questions correctly out of n questions is given by the formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the total number of questions, k is the number of questions answered correctly, and p is the probability of guessing a single question correctly.

In this case, n = 20, k ranges from 15 to 20, and p = 0.2. We need to calculate the sum of the probabilities for k = 15, 16, 17, 18, 19, and 20. Using a binomial probability calculator or a statistical software, we find that the probability of guessing at least 15 out of 20 correctly is approximately 0.0028 or 0.28%.

This event can be considered unlikely to occur because the probability is very low. The chances of randomly guessing the correct answer in a multiple-choice exam are low, and guessing correctly on at least 15 out of 20 questions is even more improbable.


Learn more about Probability in multiple-choice exams here:

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