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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

Credit: Jose Kevo
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Becky and her friends entered a drawing at a local store for a trip to an amusement park. Only the first 50 people to enter the store were allowed to participate in the drawing. Becky, Kaye, and Amy each entered their name in the drawing. How can Becky use the information to write a statement of probability about her chances of winning then express it as a fraction, decimal, and percent?

In this concept, you will learn to describe the probability of events as fractions, decimals or percents.

### Guidance

Fractions mean a part of a whole. Decimals and percents also mean a part of a whole. Therefore, probabilities can be written as fractions, decimals, or as percents.

Let’s practice writing the following probabilities three different ways.

Here is a scenario.

A bag has four cubes in it, a red cube, two yellow cubes and one blue cube. What is the probability of drawing a red or yellow cube out of the bag?

First, write a fraction to show the ratio of possible outcomes and favorable outcomes. There are four cubes in the bag, so there are four possible outcomes. This is the denominator.

\begin{align*}\begin{array}{rcl} P &=& \frac{\# \text{ of favorable outcomes}}{\# \text{ of possible outcomes}} \\ P &=& \frac{D}{4} \end{array}\end{align*}

Next, determine the favorable outcomes by counting the red and yellow cubes. There are two yellow cubes and one red cube. That means that there are three favorable outcomes.

\begin{align*}P=\frac{3}{4}\end{align*}

This is the answer as a fraction.

To convert the fraction to a decimal, find an equivalent fraction with a denominator that is a multiple of 10. In this case, the denominator will be 100. Because you have to multiply 4 by 25 to get a denominator of 100, you have to multiply the numerator by 25.

\begin{align*}\begin{array}{rcl} P = \frac{3}{4} &=&\frac{D}{100} \\ 4 \times 25 &=& 100 \\ 3 \times 25 &=& 75 \\ P &=& \frac{75}{100} \text{ or } .75 \end{array}\end{align*}

Now, take the decimal and make it a percentage. If you look at the fraction out of 100 it is already clear what the percentage is. The percentage is 75% because percent means out of 100.

If you were working with the decimal only, then you move the decimal point two places to the right and then add the % sign. You move it two places because that is hundredths and % means out of 100.

### Guided Practice

Mrs. Scott placed the names of her 10 students in a bag. There were 6 girls’ names and 4 boys’ names in the bag. What is the probability that Mrs. Scott will not pull out a girl’s name? Write this answer as a decimal and a percentage.

First, write it as a ratio.

There 10 names in the bag, so there are 10 possible outcomes. The denominator is 10. There are 4 boy names in the bag. These are the favorable outcome, so 4 is the numerator. This is the ratio.

\begin{align*}\frac{4}{10}\end{align*}

Next, convert this to a decimal by dividing the numerator by the denominator.

\begin{align*}4 \div 10 = .40\end{align*}

Then, convert this to a percentage.

.40 becomes 40% by moving the decimal two places to the right.

The answer is .40 or 40%.

### Examples

Convert the fractions to decimals and percentages in the following examples.

#### Example 1

\begin{align*}\frac{1}{4}\end{align*}

First, divide the numerator by the denominator to get a decimal.

\begin{align*}1 \div 4=.25\end{align*}

Next, convert the decimal to a percentage by moving the decimal two places to the right.

.25 becomes 25%

The answer is .25 or 25%.

#### Example 2

\begin{align*}\frac{1}{2}\end{align*}

First, divide the numerator by the denominator to get a decimal.

\begin{align*}1 \div 2=.50\end{align*}

Next, convert the decimal to a percentage by moving the decimal two places to the right.

.25 becomes 25% by moving the decimal two places to the right.

The answer is .5 or 50%.

#### Example 3

\begin{align*}\frac{5}{8}\end{align*}

First, divide the numerator by the denominator to get a decimal.

\begin{align*}5 \div 8=.625\end{align*}

Next, convert the decimal to a percentage by moving the decimal two places to the right.

.625 becomes 62.5% by moving the decimal two places to the right.

The answer is .625 or 62.5%.

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Remember Becky and her hope of winning tickets to the amusement park?

Becky read the back of the entry and learned that the winner of the drawing gets to take two friends with them to the amusement park. She’s exhales, relieved that she has a better chance of going to the amusement park because she and her two friends entered the drawing. That makes her have 3 chances instead of 1. To see how good her chances are, she decides to find the probability as a ratio, fraction, and a decimal.

First, write it as a ratio.

There are 50 entries in the drawing, so there are 50 possible outcomes. The denominator is 50. Becky gets to go to the amusement park if her entry is drawn or if one of her two friends’ entries is drawn. That makes her have 3 favorable outcomes. This is the numerator. The fraction is the ratio.

\begin{align*}\frac{3}{50}\end{align*}

Now, convert that to a decimal by dividing the numerator by the denominator.

\begin{align*}3 \div 50=.06\end{align*}

Then, convert .06 to a percent by moving the decimal two places to the right.

6%

That is the probability written as a ratio, decimal and percent.

### Explore More

A bag has the following 10 colored stones in it. There are 2 red ones, 2 blue ones, 3 green ones, 1 orange one, and 2 purple ones.

Write a decimal and a percent for each probability based on the scenario above.

1. One orange stone
2. A red stone
3. A green stone
4. A yellow stone
5. A blue stone or an orange one
6. A red one or a blue one
7. A green one or an orange one
8. A blue one or a green one
9. A blue one or a purple one
10. A purple one or a red one
11. Not purple
12. Not red
13. Not orange or purple
14. Not red or purple
15. Not orange

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