Problem

The following involves taking a multiple-choice exam and guessing on every single question. The test has 4 questions, and each question has 4 possible responses, of which only 1 is correct. Compute the following probabilities.

The probability of getting at least 2 questions correct. Write your final answer as a percent rounded two two decimal places.
Number
$\%$

Answer

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Answer

Final Answer: The probability of getting at least 2 questions correct is \(\boxed{26.17\%}\).

Steps

Step 1 :We are given a multiple-choice exam with 4 questions, each question has 4 possible answers and only 1 is correct. We are asked to find the probability of guessing at least 2 questions correctly.

Step 2 :We can use the binomial probability formula to solve this problem, which is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability of getting k successes in n trials, \(C(n, k)\) is the number of combinations of n items taken k at a time, p is the probability of success on a single trial, n is the number of trials, and k is the number of successes.

Step 3 :In this case, n=4 (the number of questions), p=1/4 (the probability of guessing a question correctly), and we want to find the probability of getting at least 2 questions correct, so we need to calculate \(P(X=2)\), \(P(X=3)\), and \(P(X=4)\) and add them together.

Step 4 :By calculating, we find that the probability of getting at least 2 questions correct is approximately 0.26171875.

Step 5 :Converting this to a percentage and rounding to two decimal places, we get 26.17%.

Step 6 :Final Answer: The probability of getting at least 2 questions correct is \(\boxed{26.17\%}\).

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