Question

Assume you are totally unprepared for a quiz but you decide to take it anyway and just guess at all of the answers. The quiz is 12 multiple choice questions each of which have 4 choices (that’s 1/4 chance of getting one right). What is the probability that you will pass the quiz if you need at least 8 questions correct in order to pass?

Select one:

a. 0.0115

b. 0.0008

c. 0.0004

d. 0.0028

Answer 1

This follows a Binomial distribution with the parameters n= 12 and p= = =0.25 The pmf of Binomial distribution: P(X=k) -() pk (1-) *** -(3) 0.25% 0.7512-* + P(x= 3) = (7) 025°o 15* = 0-0 023 89 → PLX= 9) = (63) 0.25% 0.75' = 0.000354 → P(X= 10) = (3) 0-2550 0.75? = 0.000035 → P(x=11) = (13) 0.25" 0.75' = 0.000002 → P(X=12) = (13) 0.25% 0.75º = 0.000000 A Call up to 6 decimals) .:. The probability that you will pain the quiz if you need at least 8 questions correct in order to pam. P(x>8) = P(x= 8) + P(x=9) + P(x = 10) + P(X=11) +P(x=12) = 0.002389 +0.000354+0.000035 +0.000002 +0.000000 = 0.002780 z 10.0028 → option (d)