A spinner is divided into four sections: green, blue, red and yellow. What is the probability of spinning the arrow and having it land in the green section? Write this probability as a fraction, decimal and as a percent.

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

### Probabilities as Fractions, Decimals and Percents

Probabilities can be computed in terms of ratios. Since any ratio can be turned into a fraction, decimal, or percent, you can also turn any probability into a fraction, decimal, or percent.

For instance, when you toss a number cube, the probability of rolling a “3” is:

\begin{align*}\begin{array}{rcl}
P(3) &=& \text{favorable outcomes} : \text{total outcomes} \\
P(3) &=& 1 : 6
\end{array}\end{align*}

The same probability can be written as a fraction simply by rewriting the two numbers in the ratio as the numerator and denominator of a fraction.

This is the answer in fraction form.

How can this fraction be expressed as a decimal?

The fraction can be expressed as a decimal by dividing the numerator by the denominator.

\begin{align*}\frac{1}{6} = & \overset{ \ \ 0.1666}{6 \overline{ ) {1.0000 \;}}}\end{align*}

The answer is 0.1666… or 0.167.

How can this decimal be expressed as a percent?

The decimal can be expressed as a percent by multiply the decimal by 100 since a percent is out of 100. Then, move the decimal point two places to the right to show the percent.

The answer is 16.7%.

The decimal 0.167 is equal to 16.7%.

To summarize, the probability of rolling a 3 with a number cube is 1 out of 6 and can be expressed in the following forms.

Ratio |
1:6 |

Fraction |
\begin{align*}\frac{1}{6}\end{align*} |

Decimal |
0.167 |

Percent |
16.7% |

### Examples

#### Example 1

Earlier, you were given a problem about your spinner with the four colors. You have a spinner with the colors green, blue, red and yellow. You want to determine the probability of landing on green expressed as a fraction, a decimal, and a percent.

First, write the fraction.

Green is one out of four colors. Therefore the fraction is:

Next, write the decimal.

\begin{align*}\frac{1}{4} = & \overset{ \ \ 0.25}{4 \overline{ ) {1.00 \;}}}\end{align*}

Then, write the percent.

The probability of spinning the spinner and landing on green is \begin{align*}\frac{1}{4}\end{align*}

#### Example 2

Kelly is playing a game at a carnival. She threw four out of 9 rings onto pins. If you write this as a fraction you get \begin{align*}\frac{4}{9}\end{align*}

What is it as a decimal or as a percent?

First, divide 4 by 9 to create a decimal.

\begin{align*}\frac{4}{9} = & \overset{ \ \ 0.4444}{9 \overline{ ) {4.0000 \;}}}\end{align*}

The answer is 0.4444… or 0.44.

Next, change the decimal to a percent.

The answer is 44%.

The decimal 0.44 is equal to 44%.

Kelly’s probability is about 44% or she hits the pins 44% of the time. The word “about” is used because the answer was rounded from the decimal to the percent.

#### Example 3

Write two out of five in fraction form.

Two out of five \begin{align*}= \frac{2}{5}\end{align*}

#### Example 4

Write two out of five in decimal form.

\begin{align*}\frac{2}{5} = & \overset{ \ \ 0.4}{5 \overline{ ) {2.0 \;}}}\end{align*}

The answer is 0.4.

#### Example 5

Write two out of five in percent form.

\begin{align*}\begin{array}{rcl}
\% &=& 0.4 \times 100 \\
\% &=& 40
\end{array}\end{align*}

The answer is 40%.

### Review

Answer the questions below.

A bag has 6 red marbles, 5 blue marbles, 7 green marbles, 2 white marbles, and 5 yellow marbles. Find the probability of randomly picking out one of the following.

- What is the probability in fraction form of choosing red marble?
- What is the probability in decimal form of choosing red marble?
- What is the probability of choosing red marble as a percent?
- What is the probability in fraction form of choosing blue marble?
- What is the probability in decimal form of choosing blue marble?
- What is the probability of choosing blue marble as a percent?
- What is the probability in fraction form of choosing green marble?
- What is the probability in fraction form of choosing white marble?
- What is the probability in decimal form of choosing green marble?
- What is the probability in percent form of choosing a green or blue marble?
- What is the probability in fraction form of choosing yellow marble?
- What is the probability in decimal form of choosing yellow marble?
- What is the probability of choosing yellow marble as a percent?
- Which 3 marbles together have a 60 percent chance of being chosen?
- Which 2 marbles together have a 48 percent chance of being chosen?
- Which 3 marbles together have a 0.72 chance of being chosen?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 11.9.