A short quiz has two true/false questions and one multiple choice question with four choices. A student guesses at each question. Assuming the choices are all equally likely, what is the probability that the student gets all three correct? Solution The events are independent, so P(A and B) = P(A)*P(B) --- P(2 correct on true- false) = (1/2)(1/2) = 1/4 P(1 correct mult-choice) = 1/4 ---- P(this and that) = (1/4)(1/4) = 1/16.

1. A short quiz has two true/false questions and one multiple choice question with four choices. A
student guesses at each question. Assuming the choices are all equally likely, what is the
probability that the student gets all three correct?
Solution
The events are independent, so P(A and B) = P(A)*P(B) --- P(2 correct on true-
false) = (1/2)(1/2) = 1/4 P(1 correct mult-choice) = 1/4 ---- P(this and that) = (1/4)(1/4) = 1/16