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 at least one answer is "A". [Hint: List all the outcomes of the sample space first.]
A) 7 / 9
B) 5 / 9
C) 1 / 3
D) 2 / 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 at least one answer is "A". [Hint: List all the outcomes of the sample space first.] 
A) 7 / 9
B) 5 / 9
C) 1 / 3
D) 2 / 3

Quizplus · Accepted Answer

There are 9 possible outcomes (3 choices for each of the two questions). The only outcomes where at least one answer is "A" are:

- A, A
- A, B
- A, C
- B, A
- C, A

So the probability of at least one answer being "A" is 5 out of 9 (5/9).

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