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

Question

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

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). Out of these, 3 outcomes (AA, BB, CC) have both answers the same. Therefore, the probability is 3 / 9 = 1 / 3.

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