Transcript Experimental Probability

Lesson 3.6
Core Focus on
Ratios, Rates and Statistics
Experimental Probability
Warm-Up
Determine whether each probability is impossible, unlikely,
equally likely, likely or certain.
1. You roll a 6 on a number cube.
unlikely
2. There is a 0.8 chance of rain today.
likely
3. You close your eyes or blink your eyes
at least once in the next five minutes.
certain
4. There is a 0.4 chance that the temperature will be greater than
60 degrees today. Write this probability as a percent and a
simplified fraction.
2
40%;
5
Lesson 3.6
Experimental Probability
Find and interpret the experimental
probability of an event.
Vocabulary
Outcome
One possible result from an
experiment or probability event.
Trial
A single act of performing an
experiment.
Sample Space
The set of all possible outcomes
for an event. Use { } to list a
sample space.
Experimental Probability
The ratio of the number of times
an event occurs to the total
number of trials.
Good to Know!
The notation P( ) is used for probabilities.
Example:
The probability of rolling a 2 with a number
cube is written as P(2) or P(two).
Example 1
Abram had 2 red marbles and 1 white marble in a bag. He
chose the white marble. Identify the outcome and show the
sample space for this experiment.
He chose a white marble.
Outcome: white
The possible marbles Abram could have chosen are red,
red or white.
Sample Space = {red, red, white}
Experimental Probability
number of times the outcome occurs
P(event ) 
total number of trials
Example 2
Nik took a jelly bean out of a bag without looking. He recorded
the color. He placed it back in the bag. He did this several times.
The results are shown in the table.
a. Find the total number of trials.
Find the total of the frequencies.
Nik completed 48 trials.
4 + 12 + 8 + 24 = 48
Example 2 Continued…
Nik took a jelly bean out of a bag without looking. He recorded
the color. He placed it back in the bag. He did this several times.
The results are shown in the table.
b. Find the experimental probability his next jelly bean
will be red.
number of times red is chosen
P(red) 
total number of trials
4 1
P(red) 

48 12
This is read, “The probability
of picking a red is one-twelfth.”
Example 2 Continued…
Nik took a jelly bean out of a bag without looking. He recorded
the color. He placed it back in the bag. He did this several times.
The results are shown in the table.
c. Find the experimental probability his next jelly bean
will be green.
number of times green is chosen
P(green) 
total number of trials
24 1
P(green) 

48 2
Explore!
Rolling a 3
Step 1 Copy the chart below on your paper. Roll a number cube ten times. Record the
number of times each number appears by using a tally mark in the chart.
a.
b.
How many trials have you done?
Find P(roll a 3).
Step 2 The table below shows some common fractions used when measuring in
inches. Copy the table and convert each measurement to a decimal.
a. How many trials have you done?
b. Find P(roll a 3).
Step 3 Roll the number cube ten more times.
Record the number of times each number
appears using the chart from Step 1.
a.
b.
How many trials have you done?
Find P(roll a 3).
Explore!
Rolling a 3
Step 4 Roll the number cube ten more times. Record the number of times each
number appears using the chart from Step 1. Continue adding tally marks.
a.
b.
How many trials have you done?
Find P(roll a 3).
Step 5 Roll the number cube ten more times. Record the number of times each
number appears using the chart from Step 1. Continue adding tally marks.
a.
b.
How many trials have you done?
Find P(roll a 3).
Step 6 Which probability do you think is the most accurate
estimate for the probability of rolling a 3 on your
next turn? Explain your reasoning.
Communication Prompt
Suppose you entered a contest where you will throw
bean bags through a hole in a piece of plywood as part
of a fundraiser. On the day of the contest, you will
throw the bean bag 100 times. Explain how you could
create an experiment to predict how many tosses you
will make without actually throwing the bean bag 100
times. Identify your outcomes, sample space and
number of trials.
Exit Problems
1. Identify the sample space: Tom rolls a regular six-sided
number cube.
{1, 2, 3, 4, 5, 6}
2. Sherlock put his music player on random play. It chose the
same song 3 out of the last 12 times it played a song. What is
the experimental probability it will play the same song for its
next selection?
1
or 0.25 or 25%
4
3. Charlie made 4 out of 5 free throws at basketball practice
today. What is the experimental probability he will make a
free throw at the game tonight?
4
or 0.8 or 80%
5