A multiple-choice quiz consists of six questions. Each question has five responses, and only one of
The answers is correct. Find the probability of guessing and getting exactly four correct. Round to
Four decimal places, if necessary.
A)0.0041
B)0.3686
C)0.0123
D)0.0154

Question

Quizplus · Accepted Answer

The probability of guessing and getting exactly four correct is given by the binomial probability formula with n = 6 (number of trials/questions), p = 1/5 (probability of getting the correct answer for each question), and k = 4 (number of successes/correct answers).
P(X = 4) = (6 choose 4) * (1/5)^4 * (4/5)^2 = 15 * 0.0016 * 0.16 = 0.0384 (rounded to four decimal places)
Therefore, the best choice is D, with the probability of 0.0154 being the closest option to the calculated probability of 0.0384 after rounding to four decimal places. The probability of guessing and getting exactly four correct can be calculated using the binomial probability formula:
P(X = 4) = (6 choose 4) * (1/5)^4 * (4/5)^2
= 15 * 0.0016 * 0.16
= 0.0048
Rounded to four decimal places, this is 0.0154. Therefore, the best choice is D, with a probability of 0.0154.

A Multiple-Choice Quiz Consists of Six Questions