6th Grade Math Textbook, Fundamentals

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12-3

Key Concept

Theoretical Probability Formula

P(E) 

Note that the formula is based on all possible outcomes being equally likely.

number of favorable outcomes

number of possible outcomes

Remember:To rename a fraction

as a decimal, divide the numerator

by the denominator.

To rename a decimal as a percent,

multiply the decimal by 100, and

write the percent symbol.

To find the probability of Dee selecting a package of raisins,

use the formula for theoretical probability.

P(E)  P(raisins) 

So the probability of Dee selecting a package of raisins is or 0.25 or 25%.

1

4

5

20

1

4

number of favorable outcomes

number of possible outcomes

1

4

Theoretical Probability

Objective To write probabilities as fractions, decimals, and percents• To represent

probabilities as fractions, decimals, and percents on a number line from 0 to 1• To define the

theoretical probability of an event and use a formula to find theoretical probability• To find the

theoretical probability of complementary events

Dee can choose from a grab bag of 20 small packages. There are
5 packages of raisins, 5 packages of nuts, 5 packages of trail mix,
and 5 packages of dried fruit. Dee randomly selects one package.
What is the probability that she will select a package of raisins?

The , P(E), is a measure of how likely

it is that an event will occur. Probability is represented by a

ratio that is equal to 0 or 1, or that lies between 0 and 1.

If an event is impossible, its probability is 0.

If an event is certain, its probability is 1.

Otherwise, the probability of an event is between 0 and 1.

The more likelyan event, the closer its probability will be to 1.

The less likelyan event, the closer its probability will be to 0.

Probabilities can be expressed as fractions, decimals, and percents.

You can use a number line to visualize probabilities.

Theoretical probabilityis calculated by analyzing possible outcomes

rather than by conducting an experiment. It is based on known information,

such as the number of equal sections in a spinner. It tells what should

happen in an experiment. The outcomes that you are looking for in an event

are called. The of an event is the ratio

of the number of favorable outcomes to the total number of possible outcomes.

theoretical probability

probability of an event

favorable outcomes

0 1

0.0 0.25 0.5 0.75 1.0

0% 25% 50% 75% 100%

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2

3

4

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4

Less

Impossible Likely

Equally

Likely

More

Likely Certain