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Algebra II
12.1 Probability Distributions
LEQ: How can you use a probability distribution to compare the probability of events?
Procedure:
1. Making a Probability Distribution:
a. Definition 1: A _______________________________ is a list of the
outcomes in a sample space and the number of times each outcome
occurs.
b. Example 1: Making a Frequency Table:
In the game Rock-Paper-Scissors, the scissors cut the paper, the rock
dulls the scissors, and the paper covers the rock. Use the results below to
make a frequency table for the winning players: Player 1, Player 2, or tie.
c. Definition 2: Probability over a continuous range of events is
____________________________________.
d. Example 2: Real-World Connection:
Social Science Use the frequency table. Find the probability that an
elderly person living alone will have contact with his or her children more
than once a week.
Find P(more than once a week)
Find P(once a week or more)
e. Definition 3: A _________________________________________ is a
function that gives the probability of each event in a sample space.
f. Example 3: Probability Distributions:
Use a table and a graph to show the probability distribution for the spinner
{red, green, blue, yellow}.
g. Example 4: Real-World Connection:
Genetics Use the information in the chart of inherited gene pairs. Graph
the probability distribution for each sample space.
a. Genotype Distribution
b. Plant Color Distribution
c. Which probability distribution would be more useful to a farmer who
wants to avoid raising white corn plants? Explain.
d. Make a probability distribution table for each sample space.
2. Using a Probability Distribution:
a. Example 5: Real-World Connection:
Market Research At a certain store, the number of customers c who
arrive at the checkout counter each minute varies according to the
distribution below. Simulate the number of customers over a ten-minute
period.
Step 1: Define how the simulation will be done. Use random numbers.
Assign numbers from 1 to 100 to the events, based on the probability of
each event. Use cumulative probabilities to help you assign the numbers.
(Pg. 916)
Event
Probability
0
0.15
1
0.24
2
0.28
3
0.17
4
0.09
5
0.05
6
0.02
Cumulative
Probability
Assigned
Numbers
Step 2: Conduct the simulation. Model a ten-minute period by generating
ten random numbers from 1 – 100.
Step 3: Interpret the simulation.
3. HW: pg. 651 (3 – 5, 10, 14, 16, 19)