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Measurement of Probability

Express ratio of favorable and possible outcomes as fractions, decimals, and percents.

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Measurement of Probability

Let's Think About It

License: CC BY-NC 3.0

Nathalie's teacher is holding a class lottery.  Five winners will receive a night off from homework.  There are 25 students in the class.  What is the probability of Nathalie being one of the winners who will enjoy a homework-free night?  Write the answer as a ratio, fraction, decimal, and percent.

In this concept, you will learn how to write ratios as fractions, decimals and percent.

Guidance

Ratios can be written as fractions, decimals and percents.

1:2 can be written as or as a decimal of .50 or as a percent of 50%

Because probability is written as a ratio, we can also write probabilities as fractions, decimals and/or percents.

Let's look at an example:

A bag contains 5 black ping pong balls, 8 white ping pong balls, and 7 yellow ping pong balls. What is the probability of drawing a black ping pong ball from the bag?

First, let’s look at writing the probability as a ratio:

Now that you have a ratio, you can easily take this ratio and write it as a fraction. Notice that the first value in the ratio becomes the numerator and the second number becomes the denominator.

1:4 becomes  

Next, convert the fraction to a decimal. There are two ways to do this.

The first way is to divide the numerator by the denominator.

The decimal is .25.

The second way is to write a proportion. You can convert one-fourth to a proportion out of 100.  This only works if the denominator can be converted to 100.

Now you can write it as a decimal: 0.25

Converting the decimal to a percent easy:   0.25 = 25%

.25 or

Let’s look at another one.

Remembering the bag which contains 5 black ping pong balls, 8 white ping pong balls, and 7 yellow ping pong balls, what is the probability of choosing a yellow ping pong ball?

Now, write this as a fraction.

As a decimal:

And as a percent:

A prediction is a reasonable guess about what will happen in the future. Reasonable predictions should be based on facts. For example, you might predict that it’s going to rain today. Your prediction is reasonable if it is based on facts and evidence. For example, you might base your prediction on:

  • a reliable weather report you heard
  • dark clouds in the sky
  • a satellite photo of your area
  • a phone call from a nearby friend who lives where it’s raining

The most accurate kinds of predictions are based on probability.

For example, if you assume that all 5 spinner sections in the spinner above are equal in size and, therefore, equally likely to be landed on, then the probability of spinning red is:

Since a 3 out of 5 probability is greater than 50 percent, it is reasonable to predict that the spinner is likely to land on red.

Here are some other reasonable predictions you might make.

Reasonable Prediction Reason
The spinner is more likely to land on red than blue. There are 3 red sections and only 1 blue section.
The spinner is equally likely to land on blue or yellow. There spinner has an equal number of blue and yellow sections – one each.
On the average, a ratio of about 4 of 5 spins are likely turn up blue or red. Four out of 5 sections are blue or red.
Most of the time the spinner will not land on blue or yellow. Blue and yellow combined make up fewer than half of the sections.

Not all predictions are reasonable.

Unreasonable Prediction Reason
The spinner is more likely to land on blue before it lands on red. There are fewer blue sections (1) than red sections (3).
The spinner will never land on blue before it lands on red. The spinner can land on blue before it lands on red; it just isn’t likely to occur.
Three out of every 5 spins will always be red. On the average, 3 of 5 spins will be red, but on any given series of spins anything can happen.

When making predictions, it is best to keep in mind that probability predicts only what is likely to happen. All events are subject to chance. On any given event, anything can happen. If you flip a coin 4 times, you are most likely to land on heads twice and tails twice.  However, that doesn’t mean that on any given pair of 4 flips, you might land on heads zero times, or you might land on heads 4 times. Neither event is likely, but both are possible and each will happen from time to time.

The value of probability is very limited in the short term. But over the long term, predictions based on probability are usually highly accurate.  In general, the greater the number of outcomes you have, the closer a prediction based on probability is likely to be.

Guided Practice

Joan's mom hard-boiled 4 eggs to make egg salad.  Joan saw the eggs on the counter and, not knowing they were hard-boiled, placed them back into the egg carton with the raw eggs.  There are a dozen eggs in the carton.  What is the probability that Joan's mom will choose hard-boiled eggs from the carton for her egg salad?  Write your answer as a ratio, fraction, decimal, and percent.

First, identify the favorable and total outcomes:

There are 4 hard-boiled eggs; so the favorable outcome is 4.  There are 12 eggs all together; so the total outcome is 12.

Next, create a ratio with from the result of the favorable and total outcomes.  Make sure to simplify the results.

Then, create an equivalent fraction, decimal, and percentage from the ratio:

fraction: 1:3 = 1/3 

decimal:  Since the denominator cannot be converted to 100, divide the numerator by the denominator.

  (round to the nearest hundredth)

percentage:  33%

The answer is the ratio is 1:3, the fraction is 1/3, the decimal value is 0.33, and the percentage is 33%.

Examples

Write each ratio as a fraction, decimal and percent.

Example 1

First, create a fraction from the ratio:

1:5 = 1/5

Next, create a decimal from the fraction by dividing the numerator by the denominator:

Since the denominator can be converted to 100, either create a proportion and solve for the missing value or divide the numerator by the denominator.

  or  

Then, convert the decimal into a percentage:

0.20 = 20%

The answer is the fraction is 1/5, the decimal value is 0.20, and the percentage is 20%.

Example 2

First, create a fraction from the ratio, making sure to simplify if possible: 2:4 = 2/4 = 1/2

Next, create a decimal from the fraction by dividing the numerator by the denominator:  Since the denominator can be converted to 100, either create a proportion and solve for the missing value or divide the numerator by the denominator. 

 or   

Then, convert the decimal into a percentage:0.50 = 50%

The answer is the fraction is 1/2, the decimal value is 0.50, and the percentage is 50%.

Example 3

First, create a fraction from the ratio: 4:5 = 4/5

Next, create a decimal from the fraction by dividing the numerator by the denominator:  Since the denominator can be converted to 100, either create a proportion and solve for the missing value or divide the numerator by the denominator.

   or  

Then, convert the decimal into a percentage:

0.80 = 80%

The answer is the fraction is 1/5, the decimal value is 0.20, and the percentage is 20%.

Follow Up

License: CC BY-NC 3.0

Remember Nathalie and her teacher's lottery for a homework-less night?  

Five students will be chosen from 25 total and the winners will be given a pass from homework for a night.  Figure out Nathalie's probability of being chosen  and write as a ratio, fraction, decimal, and percentage.

First, identify the favorable and total outcomes:

There will be 5 students who will win the lottery; so the favorable outcome is 5.  There are 25 students all together; so the total outcome is 25.

Next, create a ratio with equivalent fraction, decimal and percent from the result of the favorable and total outcomes.  Make sure to simplify the results.Then, create an equivalent fraction, decimal, and percentage from the ratio:

fraction:  1:5 = 1/5

decimal:  Since the denominator can be converted to 100, either create a proportion and solve for the missing value or divide the numerator by the denominator.

  or   

decimal: 0.20 = 20%

The answer is the ratio is 1:5, the fraction is 1/5, the decimal value is 0.20, and the percentage is 20%.

Video Review

Explore More

Use what you have learned about theoretical probability to answer each question.

What is the probability of the spinner landing on 9?

1. List each favorable outcome.

2. Count the number of favorable outcomes.

3. Count the total outcomes.

4. Write the probability. Simplify, if necessary.

What is the probability of the spinner landing on 3 or 4?

5. List each favorable outcome.

6. Count the number of favorable outcomes.

7. Count the total outcomes.

8. Write the probability. Simplify, if necessary.

What is the probability of the spinner landing on blue?

9. List each favorable outcome.

10. Count the number of favorable outcomes.

11. Count the total outcomes.

12. Write the probability. Simplify, if necessary.

What is the probability of the spinner landing on a silver number greater than 4?

13. List each favorable outcome.

14. Count the number of favorable outcomes.

15. Count the total outcomes.

16. Write the probability. Simplify, if necessary.

Answer each question and write the probability as a fraction, a decimal and a percent.

17. A clothes dryer contains 12 socks. What is the probability of reaching inside the dryer and pulling out a blue sock?

18. What is the probability of pulling a red sock out of the dryer?

19. What is the probability of pulling a blue or white sock out of the dryer?

20. What is the probability of pulling a blue or red sock out of the dryer?

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 12.2. 

Vocabulary

Event

Event

An event is a set of one or more possible results of a probability experiment.
Favorable Outcome

Favorable Outcome

A favorable outcome is the outcome that you are looking for in an experiment.
Probability

Probability

Probability is the chance that something will happen. It can be written as a fraction, decimal or percent.
Sample Space

Sample Space

In a probability experiment, the sample space is the set of all the possible outcomes of the experiment.
Total Outcomes

Total Outcomes

In probability, the total outcomes are the total number of possible outcomes for the probability experiment.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0

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