Title of Lesson: The Addition Rules for Probability (4.3)
Subject: Probability & Statistics
Grade level: 12th
(1) Find the probability of compound events, using the addition rules.
SCSDE Curriculum Standard(s) Addressed:
DA-1.5 Apply the principles of probability and statistics to solve problems in real-world
DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical
DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of
DA-5.7 Carry out a procedure to compute simple probabilities and compound probabilities
(including conditional probabilities).
NCTM National Curriculum Standard(s) Addressed:
Data Analysis & Probability Standard for Grades 9-12
Understand how to compute the probability of a compound event
Problem Solving Standard for Grades 9-12
Build new mathematical knowledge through problem solving
Solve problems that arise in mathematics and in other contexts
Reasoning and Proof Standard for Grades 9-12
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Representation Standard for Grades 9-12
Create and use representation to organize, record, and communicate mathematical
know how to calculate the probability of an event
be familiar with the cards in a normal deck of cards
SMART board presentation
Have students get into their groups of four to complete their Tribe Challenge (review
from previous lesson).
(1) If I roll the die one time, what is the probability that I will get an even number or
(2) Assume a normal deck of 52 cards (no jokers!) If I draw one card what is the
probability that I choose a heart or a spade?
(3) P(face card or club)?
Have students list on the board the homework questions they did not understand from
Have students volunteer to complete the homework questions on the board
Have student who completed the problem, explain the problem
If some questions are not completed or there is a confusion about a specific problem,
explain more thoroughly
Pull up the SMART board presentation on the SMART board
Ask students if they have any idea what it means to be mutually exclusive.
Explain what it means for two events to be mutually exclusive.
o Mutually exclusive means the events cannot occur at the same time.
Example 1: There is a large political event. What is the probability that the person
selected is either a democrat or a republican?
o Since a person cannot be a democrat and a republican, the events are mutually
Have students create examples of mutually exclusive events.
Example 2: What is the probability that the person is a female or is a republican?
o We have three things to consider:
(3) both female and republican
o Since a person can be a female and a republican, the events are not mutually
Have students give examples of not mutually exclusive events.
Determine which events are mutually exclusive and which are not when a single die is
o Getting an odd number and getting an even number
The events are mutually exclusive, since the first event can be 1, 3, or 5
and the second event can be 2, 4, or 6.
o Getting a 3 and getting an odd number
The events are not mutually exclusive, since the first event is a 3 and the
second can be 1, 3, or 5. Hence, 3 is contained in both events.
o Getting an odd number and getting a number less than 4
The events are not mutually exclusive, since the first event can be 1, 3, or
5 and the second can be 1, 2, or 3. Hence, 1 and 3 are contained in both
o Getting a number greater than 4 and getting a number less than 4
The events are mutually exclusive, since the first event can be 5 or 6 and
the second event can be 1, 2, or 3.
Have students work together in their tribes to determine what they must do when
calculating two or more events that are not mutually exclusive.
o Give example of the probability of selecting a card and it being a king or a club.
Assume the deck of cards is normal and does not include jokers.
o Have them try to calculate the following probability:
Getting an odd number and getting an even number
The events are mutually exclusive, since the first event can be 1,
3, or 5 and the second event can be 2, 4, or 6.
Getting a 3 and getting an odd number
The events are not mutually exclusive, since the first event is a 3
and the second can be 1, 3, or 5. Hence, 3 is contained in both
Getting an odd number and getting a number less than 4
The events are not mutually exclusive, since the first event can be
1, 3, or 5 and the second can be 1, 2, or 3. Hence, 1 and 3 are
contained in both events.
Getting a number greater than 4 and getting a number less than 4
The events are mutually exclusive, since the first event can be 5 or
6 and the second event can be 1, 2, or 3.
After allowing students to explain what happened in the following problems, work
together with them to develop a formula for finding events that are mutually exclusive
and events that are not mutually exclusive.
Play the game Rapid Fire.
o PowerPoint slides are shown with various problems.
P(heart or club), P(face or 2), P(even or 1), etc.
o The student who answers the question right first gets a point for their tribe (this
will encourage students to pay attention since they want to get points for their
“tribes”. I have found that a lot of time kids refuse to listen in class, but when
they are rewarded with points for their team they work more efficiently and the
teacher can truly engage them.
Try an application problem. Allow students to work on this question in groups towards
the end of class to assess if they fully understand the lesson.
o The probably that a customer selects a pizza with mushrooms or pepperoni is
0.43, and the probability that the customer selects mushrooms only is 0.32. If
the probability that he or she selects pepperoni only is 0.17, find the probability
of the customer selecting both items.
Have students create and turn in a Frayer Model with the word mutually exclusive:
Have students write on a sheet of paper to turn in before they leave: what they learned
today and what they did not understand from today’s lesson. Referred to as “exit slip”.
This will help me know what I need to review during the next class period.
Observing students’ answers to tribe challenge (assesses the previous lesson)
Observing students’ questions about the previous night’s homework (assesses the
Listening to students’ examples of mutually exclusive and not mutually exclusive events
Observing students’ ability to determine if a given event is mutually exclusive or not
Listening to students’ discussion when trying to discover what is going on when we
calculate the probability of two or more events that are not mutually exclusive
Notice students’ answers when answering the questions in the game Rapid Fire
Student’s ability to complete the application problem.
Students’ Frayer Model
Students’ quiz they will be given at a later date
Students’ exit slips
If some students understand these concepts quickly, I will give them more questions to extend
In building new homes, a contractor finds that the probably of a home buyer selecting a
two-car garage is 0.20. Find the probability that the buyer will select no garage. The
builder does not build house with three-car or more garages.
In the previous problem, find the probability that the buyer will not want a two-car
Suppose that P(A) = 0.42, P(B) = 0.38, and P(A U B) = 0.70. Are A and B mutually
1. A furniture store decides to select a month for its annual sale. Find the probability that
it will be April or May. Assume that all months have an equal probably of being
2. The probability that a student owns a car is 0.65, and the probability that a student
owns a computer is 0.82. If the probability that a student owns both is 0.55, what is the
probability that a student owns neither a car not a computer?
3. A particular school with 200 male students, 58 play football, 40 play basketball, and 8
play both. What is the probably that a randomly selected male student plays neither
4. If one card is draw from an ordinary deck of cards, find the probability of getting the
a. A king or a queen or a jack
b. A club or a heart of a spade
c. A king or a queen or a diamond
5. Two dice are rolled. Find the probability of getting
a. A sum of 6 or 7 or 8
b. Doubles or a sum of 4 or 6
c. A sum greater than 9 or less than 4 or a 7
(Also include the adaptation questions if they are not completed in class)