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) 1/9
B) 1/6
C) 1/3
D) 1/27

Question

Quizplus · Accepted Answer

The sample space for two questions with three answer choices each consists of 3 x 3 = 9 outcomes (AA, AB, AC, BA, BB, BC, CA, CB, CC). Among these, 3 outcomes (AA, BB, CC) have both answers the same. Therefore, the probability is 3/9, which reduces to 1/3.

A Section of an Exam Contains Two Multiple-Choice Questions, Each