Lesson 1

Lesson 1: Experimental Probability

 

Focus

 

Various levels of predicted and worst-case scenario flooding are often shown on flood maps. However, estimating flooding beyond the “100-year flood” is a difficult task, as there is a lack of historical flood information to compare.

 

Estimates of how often a flood will occur in a given time period are referred to as a “1-in-20-year flood” or “1-in-100-year flood” and are based on the amount of flooding that occurs.

 

The longer the time period, the larger the flood event. Statistically, this means that a 1-in-100-year flood will have a one percent chance of occurring in any given year. A 1-in-100-year flood would be rarer and much bigger than a 1-in-20-year flood.

 

This does not mean that if a 100-year flood happened this year, it wouldn't happen again for another 100 years. It could happen again next year, or even two or more times in any year.

 

Lesson Outcome

 

At the end of this lesson you will be able to use data to help make predictions and/or determine the probability of an event.

 

Lesson Question

In this lesson you will investigate the following question:

• How does probability affect your decisions?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you have difficulty with concepts or calculations, contact your teacher.

 

Remember that the questions and activities you will encounter provide you with the practice and feedback you need to successfully complete this course. You should complete all questions and place your responses in your course folder. Your teacher may wish to view your work to check on your progress and to see if you need help.

 

Materials and Equipment

 

You will need

• calculator
• two standard six-sided dice (virtual dice are also available in the lesson)

Launch

 

Do you have the background knowledge and skills you need to complete this lesson successfully? Launch will help you find out.

 

Before beginning this lesson you should be able to

• convert between decimals, percentages, and fractions
• find the percent of a number
• solve equations using proportional reasoning (cross multiplying)

Are You Ready?

 

Complete these questions. If you experience difficulty and need help, visit Refresher or contact your teacher.

1. Convert the percent to a decimal.
   1. 65% Answer
   2. 99% Answer
   3. 0.1% Answer
   4. 0.006% Answer
   5. 2.7% Answer
   6. 8.75% Answer
2. Calculate the percentage.
   1. 35% of $2795.00 Answer
   2. 6% of 196.00 cm Answer
   3. 0.5% of 235 000 Answer
   4. 92% of 1.75 Answer
   5. 20% of 2.35 Answer
   6. 1.75% of 10.97 Answer
3. Complete the table.
   
   

   Percent	Decimal	Fraction
   30%
   	0.24
   62.5%
   	0.2
   125%
   	0.035

   
   Answer
4. Solve for x.
   1.  Answer
   2. Answer
   3.  Answer
   4.  Answer
5. Sean gets 70% on a test consisting of 20 questions. How many questions did Sean get right? Answer
6. Assume that 60% of children will have a cellphone by the time they are fourteen years of age. In a group of 90 fourteen-year-olds, how many can you assume will have a cellphone? Answer
7. There were 24 students who took their class 5 drivers test during a particular week. Of those 24 students, 18 passed the test. What percentage of students did not pass the test? Answer

If you answered the Are You Ready? questions without difficulty, move to Discover.

 

If you found the Are You Ready? questions difficult, complete Refresher.

Refresher

 

Recall that a ratio is a comparison between two things.

 

For example, suppose a mixed ball-hockey team has 3 female players on a team of 10. How can the number of female players on this team be represented?

 

There are a few ways to express this; however, the most common way is to write a ratio in a fractional form. Here are a few ratios to represent the number of female players:

• female players to all players:
• female players to male players:

A ratio can also be expressed as a percent or a decimal.

 

Recall that percent is a ratio represented out of 100. Therefore, if there are 100 players on the team and the ratio remained consistent, what percentage of players could you assume would be female?

 

Write the ratio as equivalent fractions, with x representing the number of female players out of 100.

 

 

Therefore, x = 3 × 10 or 30.

 

 

30% written as a decimal is simply “3 divided by 10” or “30 divided by 100” which equals 0.30.

 

In summary, the number of female players on this ball-hockey team can be expressed in the following ways.

 

Percent	Decimal	Fraction
30% of the players are female	0.30	For every 10 players, 3 of them are female.

 

 

Use the "Percent, Fractions, and Decimals" gizmo, as well as the following questions, to help you further develop your understanding in connecting percents, fractions, and decimals.

1. Adjust the grid size to be 10 by 10. (Drag the handle in the lower-right corner to change the size of the grid.)
2. In your notebook, make a table like the one shown.
   
   
    

   Number of Shaded Squares	Percent	Decimal	Fraction

3. In the first column, write down five random numbers between 0 and 100.
4. Using the gizmo, shade the number of squares that you have in row one of the table.
5. Complete the table by making note of its equivalent percent, decimal, and fraction as provided in the gizmo.
6. Can you think of some strategies that will help you quickly convert percent, decimals, and fractions without using the gizmo?

Go back to the Are You Ready? section and try the questions again. If you are still having difficulty, contact your teacher.

Discover

 

How do you make decisions? Some decisions can be made quickly, while others need time for deliberation.

 

Think of a difficult choice that you have had to make recently. It might have involved choosing a cellphone, a transportation method, a computer, the date and destination for a vacation, a school, and so on.

 

How did you make the decision? Perhaps your decision was based on facts and information, prior knowledge, assumptions, and observations, or maybe you used your emotion or intuition.

 

Looking back, did you make the right decision? If you could change it, would you and why?

 

Try This 1

 

It is difficult to make decisions that affect the outcomes of the future. Making logical predictions based on data would certainly make decision making easier! Test your predicting abilities in the following activity.

 

Open Dice Roller and use it to answer the following questions.

 

 

 

 

1. Does each number on the green die have an equal chance of appearing when rolled?
2. Predict how many times each number will appear on the green die in 6 rolls. Explain your reasoning.

    

   Roll the die 6 times and record the results from the green die in a table like the one shown.

    

   Outcome	Tally
   1
   2
   3
   4
   5
   6
   Total

3. Did the results show that each number appeared once when the green die was rolled 6 times?

Now roll the die 6 more times and continue recording the results from the green die in your table.

4. How many times would you expect each number to appear after rolling a die 12 times?

5. From your results, are there any numbers on the die that have not yet appeared?

Roll the die 6 more times and continue recording the results from the green die in your table.

By now, you should have rolled the die a total of 18 times. Complete your table by adding a frequency column as seen in the hint. Once you are finished rolling the die, fill in the frequency column of your table. Your table should have 18 rolls of the green die.

 

Save your responses in your course folder.

 

Share 1

 

With a partner or in a group, share the results of your table and responses to the previous questions.

1. Were the frequencies of the outcomes the same? Explain.
2. Create a new table containing the combined results from your partner’s table or each group member’s table. Determine the sum of the frequency column. What does that number tell you?
3. From this new table, how many times would you expect any particular number to occur? Is this the same for each number 1 through 6?
4. Describe a way you could numerically represent the likelihood of a 2 occurring when you roll a standard 6-sided die once.

Save your shared responses in your course folder.

Explore

 

Your table of results from Share 1 may have resembled the one shown.

 

Outcome	Frequency
1	5
2	9
3	6
4	11
5	4
6	1
Total	36

 

The total of the frequency column represents the total number of times the die was rolled, or the number of possible outcomes.

 

Looking at the example table given, what was the chance of rolling a 5? What was the chance of rolling a 1?

A word that can easily replace chance is probability.

 

If the probability is determined from an experiment, such as rolling a die many times and making a frequency table, then it is called experimental probability. The activity you did in Discover was an example of experimental probability.

 

In Try This 2 you will show the different ways of representing probabilities.

 

Try This 2

 

Outcome	Frequency
1	5
2	9
3	6
4	11
5	4
6	1
Total	36

 

The following table expresses the experimental probability of each of the outcomes from rolling one die using the preceding frequency table.

 

The probabilities are in the form of fractions, decimals, percentages, and words.

 

Copy and complete the table by filling in the missing blanks. Round the decimal to the nearest thousandth. The first row has been done for you.

 

EXPERIMENTAL PROBABILITY
Outcome	Fraction	Decimal	Percentage	Words
1		0.139	13.9%	5 out of 36
2
3			17%
4		0.31
5
6				1 out of 36

 

Save your responses in your course folder.

In Try This 2 you found that probabilities can be expressed as fractions, decimals, percentages, and in words. Now try Self-Check 1 to test your abilities in demonstrating these skills.

 

Self-Check 1

Self-Check 2

 

An experiment is performed that consists of spinning a spinner and recording the results.

 

 

The results from 40 spins are recorded in the following table.

 

Outcome	Frequency
yellow	23
green	6
blue	11
Total	40

1. Express each question outcome in a different way, such as a fraction, decimal, or percent.
   1. What is the experimental probability of the spinner landing on yellow? Answer
   2. What is the experimental probability of the spinner landing on green? Answer
   3. What is the experimental probability of the spinner landing on blue? Answer
2. If the spinner was spun 120 times, how many times would you expect it to land on yellow? Answer

In Try This 3 the probability that a media player was defective was determined by the ratio which is equal to or 0.010 36.

 

The probability determined in the random sample can be used to estimate the number of defective media players in the larger group of 12 000.

 

Compare the following two strategies to arrive at your solution.

 

Strategy 1

Multiply the total number of media players by the probability.

Strategy 2

The proportion of defective media players in the random sample should be the same as the proportion of defective media players in the entire production run.

 

Based on the results from the random sample, in a production run of 12 000 media players, it can be expected that approximately 124 will be defective.

 

Try This 4

Self-Check 3

Self-Check 4

Connect

 

Lesson 1 Assignment

Lesson 1 Summary

 

In this lesson you looked at examples of experimental probability and made decisions pertaining to the chance of an event occurring, such as the chance of a flood in the next 100 years. Experimental probability is based on past experiments to help decide whether a specific outcome may or may not occur. In the next lesson you will begin to explore theoretical probabilities. These probabilities are determined without conducting an experiment or looking at previous data.