Question

Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random answer generator to determine which of true or false would be the correct answer for each quiz question, but his internet is not working. Instead, he writes each possible answer combination on a small slip of paper, folds each paper in half, and then places them in a box. Without looking, he draws one of the slips of paper.

Use what you know about counting methods and set operations to answer the following questions.

1. Let the possible quiz answer combinations represent Mr. Montes’ sample space. How many outcomes are in the sample space? Explain your answer.

2. List the outcomes in the sample space. Let T = True and F = False.

After grading the quizzes, Mr. Montes decides that his students could use some additional practice with the concepts tested. He writes a take-home assignment for his students. The assignment starts with two true or false questions and then has 3 multiple choice questions. The multiple choice questions each have 4 answer options, only 1 of which is correct. Luckily, Mr. Montes’ internet is working when he writes the quiz and he is able to use a random answer generator.

3. Let the possible answer combinations represent Mr. Montes’ sample space. How many outcomes are in the sample space? Explain your answer.

4. List 5 outcomes that are in this sample space.

5. Create a tree diagram to show the possible answer combinations of the first three questions on the take-home assignment.

6. How many possible outcomes are shown on your tree diagram? Explain.

Answer 1

The sample space of the outcomes of an event can be represented as a list and on a tree diagram

The possible quiz answer combination

From the question, we have:

Questions = 3

Options = 2 (True or False)

So, the number of outcomes in the sample space is calculated as:

$n = 2^3$

Evaluate the exponent

$n = 8$

Hence, the number of outcomes in the sample space is 8

The outcomes

Represent T = True and F = False.

So, the possible outcomes are:

Outcomes = {TTT, TFT, TTF, TFF, FTT, FFT, FTF, FFF}

The possible answer combinations

From the question, we have:

2 true or false questions

3 multiple choice questions with 4 options

So, the number of outcomes in the sample space is:

$n = 2^2 * 4^3$

Evaluate

$n = 256$

Hence, the number of outcomes are in the sample space is 256

List 5 outcomes

The possible outcomes are:

Outcomes = {TTTAA, TFTAB, TTFAC, TFFAD, FTTBA}

The tree diagram

See attachment

Possible outcomes are on the tree diagram

The possible outcomes are on the tree diagram is 8

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