If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.
A) 0.085
B) 0.218
C) 0.190
D) 0.162

Question

Quizplus · Accepted Answer

The probability can be calculated using the binomial probability formula, which is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials (20 questions), k is the number of successes (4 correct answers), p is the probability of success on a single trial (1/4, since there are 4 options per question), and (nCk) is the combination of n items taken k at a time. Plugging in the values, we get P(X = 4) = (20C4) * (1/4)^4 * (3/4)^(16), which calculates to approximately 0.190.

If a Student Randomly Guesses at 20 Multiple-Choice Questions, Find