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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:
https://brainly.com/question/26544800
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