Chapter 10
10.3: Approximating Probability and Relative Frequency
Objective…
Key Vocabulary…
Relative Frequency
Observed Frequency
Experimental Probability
Theoretical Probability
Part A: Find the Relative Frequency in a Chance Process
• Use relative frequency as a fraction
1)
The table shows the relative frequencies of men, women, and
children at a park on a particular day. On that day, 600 people
where in the park.
a. How many children were at
the park?
b.
How many more men than
women were at the park?
Chapter 10
10.3: Approximating Probability and Relative Frequency
2)
The table shows the relative frequencies for three sizes of
monitor sold during a sale at a computer store. 640 monitors were
sold during the sale.
a. How many 17-inch monitors were sold during the sale?
b. How many fewer 14-inch monitors were sold than 15-inch
monitors?
Part B: Find the Relative Frequency from a Frequency Histogram
• Use a frequency histogram to solve problems
1)
At some schools, a grade point average is used to describe
academic progress. The histogram shows data about the GPAs of
400 students at a school.
a. What is the relative frequency of students whose GPA is at
least 3? Give your answer as a fraction.
b. Find the relative frequency of students whose GPA is greater
than or equal to 3, but less than 3.5. Give your answer as a
percent.
Chapter 10
10.3: Approximating Probability and Relative Frequency
c. Draw a relative frequency histogram using percent.
2)
Alexis and Joe caught 40 fish over the weekend. The histogram
shows the masses of the fish they caught. On the histogram, the
interval 14-16 includes data for fish that has a mass of at least 14
kilograms, but less than 16 kilograms.
a. Find the relative frequency for fish that has a mass of at least
8 kilograms but less than 10 kilograms. Give your answer as a
percent.
b. Draw a relative frequency histogram using percent.
Chapter 10
10.3: Approximating Probability and Relative Frequency
Part C: Use a Relative Frequency as a Probability
Use a relative frequency as an experimental probability to make a
prediction
1)
You spin the spinner shown 200 times and record the letter that
the pointer lands on. The data are summarized below.
•
a. Find the relative frequency for each of the letters. Write each
relative frequency as a decimal.
b. If you spin the spinner again, which letter would you predict is
the spinner most likely to land on? Explain your answer.
c. What is the experimental probability that the spinner will not
land on letter D on the next spin?
2)
Lucas made a dartboard as shown in the diagram. He threw a dart
at the dartboard 100 times. He recorded the number of times the
dart landed on each color. The number of times he missed hitting
the dartboard was also recorded.
Chapter 10
10.3: Approximating Probability and Relative Frequency
a. Find the relative frequency for each of the events. Write each
relative frequency as a decimal.
b. Explain what the relative frequency of the dart landing in the
red region means.
c. If Lucas throws the dart again, predict in which region the dart
is most likely to land.
Part D: Compare Long-Run Relative Frequency and Theoretical Probability
Experimental Probability
Theoretical Probability
Try experiment!
• Place the 10 counters into the bag. Shake the bag to mix the
counters. Without looking into the bag, select a counter randomly.
Record its color in a tally chart, and then put the counter back in the
bag. Repeat this procedure 20 times.
o Repeat for each group member!
Chapter 10
10.3: Approximating Probability and Relative Frequency
o Complete relative frequency table:
Color
Observed
Frequency
Red
Relative Frequency
(as a decimal)
Blue
Green
o Find the theoretical probability for the colors by completing
the table:
Color
Theoretical
Experimental
Probability
Probability
Red
Blue
Green
o Compare the theoretical probability and the experimental
probability. What do you observe?