# Lesson 7Slacker’s SimulationSolidify Understanding

## Jump Start

Find the following:

### 1.

The probability that a fair coin is tossed twice and lands on heads both times.

### 2.

The probability that a spinner with colors (red, blue, green, yellow, pink, and orange) lands on red, and then a coin is flipped and it lands on tails.

## Learning Focus

Perform a simulation to determine if an event can occur.

Is there a way to test a claim without performing a study on actual subjects?

## Open Up the Math: Launch, Explore, Discuss

I know a student who forgot about the upcoming history test and did not study at all. To protect his identity, I’ll just call him Slacker. When I reminded Slacker that we had a test in the next class, he said that he wasn’t worried because the test has true/false questions. Slacker said that he would totally guess on every question, and since he’s always lucky, he thinks he will get at least out of . That’s what he did on the last quiz and it worked great.

I’m skeptical, but Slacker said, “Hey, sometimes you flip a coin and it seems like you just keep getting heads. You may only have a chance of getting heads, but you still might get heads several times in a row. I think this is just about the same thing. I could get lucky.”

### 1.

What do you think of Slacker’s claim? Is it possible for him to get out of questions right? Explain.

I thought about it for a minute and said, “Slacker, I think you’re on to something. I’m not sure that you will get on the test, but I agree that the situation is just like a coin flip. It’s either one way or the other and they are both equally likely if you’re just guessing.” My idea is to use a coin flip to simulate the T/F test situation. We can try it many times and see how often we get out of questions right. I’m going to say that if the coin lands on heads, then you guessed the problem correctly. If it lands on tails, then you got it wrong.

### 2.

Try it a few times yourself. To save a little time, just flip coins at once and count up the number of heads for each test.

# Incorrect (Tails)

% Correct

Test 1

Test 2

Test 3

Test 4

Test 5

Did you get out of correct in any of your trials?

### 3.

Based on your trials, do you think Slacker is likely to get correct?

### 4.

Check out the histogram that represents the data from the whole class. Now what do you think of Slacker’s chances of getting correct? Explain why.

Pause and Reflect

### 5.

What would you expect the graph to look like if you continued to collect samples? Why?

### 6.

Based upon your understanding of this distribution, what would you estimate the likelihood of Slacker getting on the test without studying?

Padma has been playing a board game with her friends where the moves are determined by the sum of the numbers on three number cubes. In the last game, one of Padma’s friends needed to roll a sum of on the cubes to win and it took her a lot of turns to get it. One of the players remarked, “I don’t know why it took so long, since is no more or less likely than any of the other numbers between and .” Padma decided to investigate this claim with a simulation. She rolled number cubes times and got this distribution:

#### a.

Which of these statements are true about rolling in this game?

#### A.

It is not possible to roll 5 in this game.

#### B.

It is not very likely to roll in this game.

#### C.

Rolling is less likely than rolling in this game.

#### D.

Rolling is less likely than rolling .

#### E.

Rolling and rolling have the same likelihood.

Simulation:

## Lesson Summary

In this lesson, we used simulation to model the outcome of a random event. Using many trials, we created a distribution and used it to predict the likelihood of an event.

## Retrieval

### 1.

• What kind of numbers are and ?

• What kind of number is ?

• What kind of number is the product of and ?

### 2.

In a group of students, are taking algebra, are taking biology, and are taking both algebra and biology.

#### a.

Draw a Venn diagram to represent this information.

#### b.

If a student, chosen at random, is taking algebra, what is the probability that he or she is taking biology? (Let be algebra and biology.)

#### c.

Which notation means the same thing as the question in part b?