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Numerical Computations

Practice working with probability in story problems

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Practice Numerical Computations
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Write and Compare Probabilities as Fractions, Decimals and Percents

Have you ever written probabilities in fraction form? How about as a decimal or a percent? Take a look at this dilemma.

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?

Can you write this probability as a fraction, decimal and percent? By the end of this Concept, you will know how to accomplish this task.

Guidance

You’ve seen how to compute probabilities 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:

You can write the same probability as a fraction simply by rewriting the two numbers in the ratio as the numerator and denominator of a fraction.

\begin{align*}P(3)=\frac{1}{6}\end{align*}

This is the answer in fraction form.

How can we turn this fraction into a decimal?

You can turn a fraction into a decimal by dividing the numerator by the denominator.

How can we turn the decimal into a percent?

We can turn a decimal into a percent by multiply the decimal by 100 since a percent is out of 100. Then we can move the decimal point two decimal places to show the percent.

\begin{align*}0.167 = 0.167 \times 100 = 16.7\%\end{align*}

To summarize, the probability of rolling a 3 with a number cube is 1 out of 6, or:

ratio fraction decimal percent
1:6 \begin{align*}\frac{1}{6}\end{align*} 0.167 16.7%

Write two out of five in different forms.

Example A

As a fraction

Solution: \begin{align*}\frac{2}{5}\end{align*}

Example B

As a decimal

Solution: \begin{align*}0.4\end{align*}

Example C

As a percent

Solution: \begin{align*}40\%\end{align*}

Now let's go back to the dilemma from the beginning of the Concept.

First, we can write the fraction.

Green is one out of four colors. That is our fraction.

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

Now let's change it to a decimal.

\begin{align*}\frac{1}{4} = \frac{25}{100} = .25\end{align*}

Next, a percent.

\begin{align*}.25 = 25\%\end{align*}

Our work is now complete.

Vocabulary

Probability
a mathematical way of calculating how likely an event is to occur.
Favorable Outcome
the outcome that you are looking for
Total Outcomes
all of the outcomes both favorable and unfavorable.

Guided Practice

Here is one for you to try on your own.

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

What is it as a decimal or as a percent?

Solution

First, we can use division to divide 4 by 9 to create a decimal.

Then we get \begin{align*}.44444...\end{align*}.

We can round that number to \begin{align*}0.44\end{align*}.

Next, we change the decimal to a percent.

\begin{align*}0.44\end{align*} becomes \begin{align*}44\%\end{align*}

Kelly's probability is about 44%. We say "about" because we rounded our number.

Practice

Directions: Use what you have learned about probability, fractions, decimals and percents to answer each question.

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.

1. What is the probability in fraction form of choosing red marble?
2. What is the probability in decimal form of choosing red marble?
3. What is the probability of choosing red marble as a percent?
4. What is the probability in fraction form of choosing blue marble?
5. What is the probability in decimal form of choosing blue marble?
6. What is the probability of choosing blue marble as a percent?
7. What is the probability in fraction form of choosing green marble?
8. What is the probability in fraction form of choosing white marble?
9. What is the probability in decimal form of choosing green marble?
10. What is the probability in percent form of choosing a green or blue marble?
11. What is the probability in fraction form of choosing yellow marble?
12. What is the probability in decimal form of choosing yellow marble?
13. What is the probability of choosing yellow marble as a percent?
14. Which 3 marbles together have a 60 percent chance of being chosen?
15. Which 2 marbles together have a 40 percent chance of being chosen?
16. Which 3 marbles together have a 0.72 chance of being chosen?

Vocabulary Language: English

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.