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 neither of the answers is "B".
[Hint: List all the outcomes of the sample space first.]
A) 4 / 9
B) 2 / 3
C) 5 / 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 neither of the answers is "B". 
[Hint: List all the outcomes of the sample space first.] 
A) 4 / 9
B) 2 / 3
C) 5 / 9
D) 1 / 3

Quizplus · Accepted Answer

There are 3 possible outcomes for each question: A, B, or C. Therefore, there are 3 x 3 = 9 total outcomes in the sample space. We want to find the probability that neither answer is B.

There are two cases to consider:

Case 1: The first question is not B and the second question is not B.

Probability of first question not being B: 2/3
Probability of second question not being B, given that the first question was not B: 2/3
Probability of both questions not being B: (2/3) x (2/3) = 4/9

Case 2: The first question is B and the second question is not B.

Probability of first question being B: 1/3 
Probability of second question not being B, given that the first question was B: 2/3 
Probability of both questions not being B: (1/3) x (2/3) = 2/9

The probability that neither answer is B is the sum of these two probabilities:

4/9 + 2/9 = 6/9 = 2/3

Therefore, the answer is A) 4 / 9

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