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.]

Answer 1

`p = (4)/(9)`

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Sample space:

All posible outcomes.

First answer - Second answer:

A - A

A - B

A - C

B - A

B - B

B - C

C - A

C - B

C - C

9 possible outcomes.

Probability that neither is B.

A - A

A - C

C - A

C - C

4 possible outcomes.

So

`p = (4)/(9)`