Question

A student (who has not studied) is expected to get 60% of multiple choice questions correct. Assume that he takes a test with 10 multiple-choice questions and there are four choices per question, and he has no idea of which of the four are correct or incorrect. (a) What is the probability of the following results:

(2) He gets at most three questions correct? .216

(3) He gets at least six questions correct?

Answer 1

P(correct answers) = 0.60

X =no of correct answers

(2) P(at most 3 correct answers) = P(x <=3) = P(0) + P(1) + P(2) + P(3)

P(x <=3) = P(0) + P(1) + P(2) + P(3) = 0.05476

P(at most 3 correct answers) = 0.055

(3) P(atleast 6 correct) = P(6) + P(7) + P(8) + P(9) + P(10) = 1- [P(0) + P(1) + P(2) + P(3) + P(4) + P(5)]

[P(0) + P(1) + P(2) + P(3) + P(4) + P(5)] = 0.36696

P(atleast 6 correct) = 1- 0.36696 = 0.63304

P(atleast 6 correct) = 0.633