A student takes a 10-question, multiple-choice exam with three choices for each question and guesses on each question. Find the probability of guessing exactly 4 out of 10 correctly.
A) 0.772
B) 0.333
C) 0.400
D) 0.228

Question

Quizplus · Accepted Answer

The probability of guessing correctly for each question is 1/3, and the probability of guessing incorrectly is 2/3. Since the student is guessing on every question, the probability of guessing exactly 4 out of 10 correctly can be found using the binomial probability formula:

P(X = 4) = (10 choose 4) * (1/3)^4 * (2/3)^6

Using a calculator or a binomial probability table, this simplifies to:

P(X = 4) = 0.228

Therefore, the best choice is D.

A Student Takes a 10-Question, Multiple-Choice Exam with Three Choices