6th Grade Math Textbook, Fundamentals

 &KDSWHU

12-4

Key Concept

Experimental Probability Formula

Exp P(E) number of times an event occursnumber of trials

Experimental Probability

Objective To find the experimental probability of an event • To find, record, and predict

outcomes of probability experiments • To simulate events to predict probability

Jay, Bailey, and Celeste are playing a board game with a 1–6
number cube. As each player rolls the cube, Jay keeps track of
which number is rolled. Based on the results shown in the table
below, about how many times in 210 trials will any player roll a 6?

123456

2525 15 23

To predict the number of times a 6 will be rolled in 210 trials,
find the experimental probability. Then write and solve a proportion.

 is the ratio of the number of times an event

occurs to the total number of trials. It serves as an estimate that an event

will happen based on how often the event occurs after collecting data from

an experiment. Unlike theoretical probability, which analyzes the outcomes

in a sample space, experimental probability analyzes the results of one or

more experiments. Each time an experiment is performed, it is called a.

As the number of trials increases, the closer each experimental probability

will be to the theoretical probability.

trial

Experimental probability

Theoretical probability is the number of times

an event shouldoccur in an experiment.

Experimental probability is the number of times

an event actuallyoccurs in an experiment.

• Find the number of times a 6 was rolled: 3 times
  Add the tally marks to find the number of trials: 2  5  2  6  7  3  25
  Write the experimental probability of the event:

P(rolling a 6) 

• Write and solve a proportion to predict the number of times
  Jay, Bailey, and Celeste will roll a 6 in 210 trials.
  Letxthe number of times 6 will be rolled.



3 • 210 25 • x Cross multiply.

630  25 x Simplify.

 Divide both sides by 25.

25.2 x

25 x Round to the nearest whole number.

So Jay, Bailey, and Celeste should expect to roll the number 6 about 25 times in 210 trials.

25 x

25

630

25

3

25

number of times an event occurs

number of trials

x

210

3

25

The number of times 6 is expected to be rolled.

new number of trials

The number of times 6 was rolled.

original number of trials