A multiple-choice exam offers five choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer right. One of your math major friends tells you that the assignment of probabilities to the number of questions Jason gets right out of 10 is (rounded to three decimal places):

What is the expected number of right answers Jason will get if the test has 10 questions?
A) 2.282
B) 2.493
C) 3.5
D) 5
E) Can't tell from the information given.

Question

A multiple-choice exam offers five choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer right. One of your math major friends tells you that the assignment of probabilities to the number of questions Jason gets right out of 10 is (rounded to three decimal places) :

What is the expected number of right answers Jason will get if the test has 10 questions?

What is the expected number of right answers Jason will get if the test has 10 questions?
A) 2.282 
B) 2.493 
C) 3.5 
D) 5 
E) Can't tell from the information given.

Quizplus · Accepted Answer

The expected number of right answers is the sum of the products of each possible number of correct answers and its corresponding probability. Thus, E(X) = 0.002(0) + 0.018(1) + 0.087(2) + 0.235(3) + 0.336(4) + 0.250(5) + 0.084(6) + 0.008(7) ≈ 2.493. Therefore, the best choice is B.

A Multiple-Choice Exam Offers Five Choices for Each Question