Download Compound Event Probability

Lesson Plan: Feb 23
Unit Title
Samantha Bruner and Rachel Volk
Statistics and Probability
Subject Area
7th grade Mathematics
Lesson Title
Compound Events using Organized List and Tree Diagrams
Audience Description
24 7th grade students
Lesson Length
35 minutes
Objectives
SWBAT:
a. Define simple and compound events of probability.
b. Draw a diagram: an organized list and a tree diagram.
c. Find the probability of a compound event.
8. Find probabilities of compound events using organized lists, tables,
tree diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space for
which the compound event occurs.
b. Represent sample spaces for compound events using methods such as
organized lists, tables and tree diagrams. For an event described in
everyday language (e.g., “rolling double sixes”), identify the outcomes
in the sample space which compose the event.
c. Design and use a simulation to generate frequencies for compound
events. For example, use random digits as a simulation tool to
approximate the answer to the question: If 40% of donors have type A
blood, what is the probability that it will take at least 4 donors to find
one with type A blood?
Standards/Benchmarks
Anticipatory Set
5 minutes
Lesson Activities
(Content/Methods and
Procedures)
25 minutes
All of the notes section will be
a class discussion format.
Class discussion reviewing the material from the previous lessons on
probability.
1. Ask the students for examples of probability, like the ones we
have been working on in the past lessons. Rachel will write
them on the board.
2. Sam will explain how these are simple events. Rachel will
connect the student’s examples of simple events to make one
compound event while explaining what a compound event is.
Then move into the lesson.
Hand out notes to students.
Go over the notes. Questions and comments to ask or add to the notes
are below.
-Simple event:
a. Example for SE: Hair color. P(girl in class), P(blonde in class)
-Compound event: go over definition. Add the comment: “For
example, you draw twice in a compound event, in a simple event you
would only draw once.”
a. Examples for a CE: Number cubes and a deck of cards.
P(6 and Jack), P(3 and a face card).
b. P(blonde and a girl in class)
c. Ask what is the first event, what is the second event? Have
them identify number of event?
d. P(girl and brunette and wearing blue)
Is this a compound event? Simple event? Neither?
-Organized list and tree diagram
a. Multiply across to find the probability of the compound event.
b. All the probabilities added together will equal 1. Check work with
this rule.
c. Ask a couple of probabilities with the example. For example,
P(red and blue) (KU colors) or P(red and green) (Christmas
colors).
-Question 2.
a. Ask which diagram they would like to use. Work through with the
students, draw the diagram and find the probabilities.
b. Answer the probability questions.
Introduce the activity:
a. First, the students will use the coin and number cube to find the
actual probability and record results.
b. They will flip and roll 12 times for their results in groups of three.
If time permits, flip and roll another 12 times to get a total of 24.
One student flips the coin, next rolls the number cube, the last
students records and repeat till they have the number of results
they need.
c. Next, the students will fill out the worksheet with the organized
list or tree diagram showing them what the expected probability is.
d. Compare to expected probability to the observational probability
as a class.
Closure
5 minutes
Hand out exit slip and allow time for the students to finish and hand it
in before the bell. Then, introduce that tomorrow’s lesson will be on
replacement probability.
Evaluation/Assessment
Exit slip: the students will make their own probability. We will assess
their tree diagram or organized list. We will also grade on their
calculation for their probabilities and following the steps of the exit
slip.
Coin, number cube, printed notes for students, guided notes for teacher,
writing utensil, and Elmo/chalkboard to present.
Resources
Unit: Statistics and Probability
Name:
Topic: Compound Events: Organized lists and Tree diagrams
Date:
Probability of a chance event is represented by the ratio: _______________
Simple event consists of exactly one outcome.
Compound event consists of two or more events.
Note: The short hand for probability of an event you can use is P(event). For
example, the probability to get an even number would be P(even).
1. Marbles: You have two bags of marbles. One bag contains 4 red marbles and 2 yellow marbles.
The other bag contains 3 blue marbles and 5 green marbles.
a. Organized List
b. Tree diagram
2. Spinner and number cube: You have a spinner with 4 colors
on it and a number cube with the numbers 1, 1, 1, 2, 3, 3.
a. P(red, 2) =
b. P(green,1) =
c. P(black,3) =
d. P(any color, number 1-3) =
1
Compound Events Activity
1. Using the coin and your number cube, flip your coin and roll your number cube 12 times. Record
your results below.
Coin
Number Cube
2. Now draw an organized list and a tree diagram of the expected probability for the compound
event that just occurred. Write the probability for each possible outcome, check your work with
the sum of the probabilities.
Exit Slip
Make your own:
e. Think of a compound probability,
f. Represent it by either an organized list or a tree diagram
g. List all probabilities in event, include checking your work by finding the sum of your
probabilities
h. Explain why it is a compound event
Exit Slip
Make your own:
a. Think of a compound probability,
b. Represent it by either an organized list or a tree diagram
c. List all probabilities in event, include checking your work by finding the sum of your
probabilities
d. Explain why it is a compound event
Exit Slip
Make your own:
i. Think of a compound probability,
j. Represent it by either an organized list or a tree diagram
k. List all probabilities in event, include checking your work by finding the sum of your
probabilities
l. Explain why it is a compound event
Exit Slip
Make your own:
e. Think of a compound probability,
f. Represent it by either an organized list or a tree diagram
g. List all probabilities in event, include checking your work by finding the sum of your
probabilities
h. Explain why it is a compound event