A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are the same ("AA", "BB" or "CC"). [Hint: List all the outcomes of the sample space first.]
A) $1 / 27$
B) $1 / 3$
C) $1 / 9$
D) $1 / 6$

Question

Quizplus · Accepted Answer

The sample space for two questions with three answer choices each consists of 3 x 3 = 9 outcomes. The favorable outcomes where both answers are the same are "AA", "BB", and "CC", totaling 3. Therefore, the probability is 3 / 9 = 1 / 3.

A Section of an Exam Contains Two Multiple-Choice Questions, Each 1/271 / 271/27

A Section of an Exam Contains Two Multiple-Choice Questions, Each $1 / 27$