A multiple-choice test has 28 questions and 3 choices for each question. If a student is totally unprepared and guesses on each question, what is the probability that she will answer 15 questions correctly? Round your answer to four decimal places.
A)0.0067
B)0.0134
C)0.0089
D)0.0149
E)0.0206

Question

A multiple-choice test has 28 questions and 3 choices for each question. If a student is totally unprepared and guesses on each question, what is the probability that she will answer 15 questions correctly? Round your answer to four decimal places. ​
A)0.0067
B)0.0134
C)0.0089
D)0.0149
E)0.0206

Quizplus · Accepted Answer

The probability of guessing one question correctly is 1/3, and the probability of guessing one question incorrectly is 2/3. To answer 15 questions correctly, the student must answer 13 questions incorrectly. Therefore, the probability is (1/3)^15 * (2/3)^13 * 28C15 = 0.0134 (rounded to four decimal places), where 28C15 is the number of ways to choose 15 questions out of 28.

A Multiple-Choice Test Has 28 Questions and 3 Choices for Each