Get out your ISN!
Today’s Objectives:
You will be able to illustrate mutually
exclusive with a Venn Diagram.
You will be able to find the probability
of 𝑨 𝒐𝒓 𝑩 using the Addition Rule.
Warm Up
Example: Ask you to pick a number
between 1 and 5, and then flip a coin.
1. Draw a tree diagram to illustrate.
2. Write out the Sample Space, 𝑆 ={
3. Find 𝑃(4𝐻).
4. Find 𝑃(𝑓𝑙𝑖𝑝𝑝𝑖𝑛𝑔 𝑎 𝑡𝑎𝑖𝑙𝑠).
}
TOC
31-32 Mutually Exclusive &
Addition Rule
WWK
Mutually Exclusive—two events are mutually
exclusive if they CANNOT occur at the same time.
NOT Mutually Exclusive—two events that CAN occur
at the same time.
Addition Rule of Probability—a way to find the
probability that either or both of two events occurs.
Big Picture
Addition Rule of
Probability
The Addition Rule of Probability is
the focus of today’s lesson.
This Rule works with the concept of
Mutually Exclusive/NOT Mutually
Exclusive.
The relationship is crucial!
Venn Diagrams
Mutually
Exclusive
NOT
Mutually
Exclusive
NO COMMON
OUTCOMES
THE COMMON
OUTCOME
Fold it in half.
Do NOT cut
anything!
foldable
FRONT
INSIDE
Foldable
Extra Practice
Circle which of the following are
mutually exclusive.
1. Red card and a Heart
2. Ace and Diamond
3. Club and Spade
4. Number 2-10 and Black
Can a Jack and a 7 happen at the
same time on the same card?
ANSWER: NO, therefore it is Mutally Exclusive
𝑷(𝑨𝒐𝒓𝑩) = 𝑷(𝑨) + 𝑷(𝑩)
𝑷 𝑱𝒂𝒄𝒌 𝒐𝒓 𝟕 = 𝑷 𝑱𝒂𝒄𝒌 + 𝑷 𝟕
=
𝟒
𝟓𝟐
𝟖
=
𝟓𝟐
+
𝟒
𝟓𝟐
Can a Heart and an Ace happen
at the same time on the same card?
ANSWER: YES, therefore it is NOT Mutally Exclusive
𝑷 𝑨𝒐𝒓𝑩 = 𝑷 𝑨 + 𝑷 𝑩 − 𝑷(𝒃𝒐𝒕𝒉)
Why is this necessary?
𝑷 𝑯𝒆𝒂𝒓𝒕 𝒐𝒓 𝑨𝒄𝒆 =
𝑷 𝑨 + 𝑷 𝑩 − 𝑷(𝒃𝒐𝒕𝒉)
Do you see how there are
TWO Ace’s of Hearts?
We have to
subtract ONE
of them so
there isn’t a
DOUBLE.
Can a Heart and an Ace happen
at the same time on the same card?
𝑷 𝑨𝒐𝒓𝑩 = 𝑷 𝑨 + 𝑷 𝑩 − 𝑷(𝒃𝒐𝒕𝒉)
𝒐𝒇
𝑷 𝑯𝒆𝒂𝒓𝒕 𝒐𝒓 𝑨𝒄𝒆 = 𝑷 𝑯𝒆𝒂𝒓𝒕 + 𝑷 𝑨𝒄𝒆 − 𝑷( 𝒂𝒄𝒆
𝒉𝒆𝒂𝒓𝒕𝒔)
=
𝟏𝟑
𝟓𝟐
+
𝟏𝟔
=
𝟓𝟐
𝟒
𝟓𝟐
−
𝟏
𝟓𝟐
Foldable
(ME)→
(NOT)→
Practice Problems
(ME)
(NOT)
Practice Problems
(ME)
(NOT)
Practice Problems
(ME)? or (NOT)?
(ME)? or (NOT)?
Practice Problems
(NOT)
(NOT)
Practice Problems
(ME)? or (NOT)?
(ME)? or (NOT)?
Practice Problems
(ME)? or (NOT)?
(ME)? or (NOT)?
Mutually Exclusive &
Addition Rule
32
11/12
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Right
Side
Input
Mutually Exclusive &
Addition Rule
31
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11/12
Left
Side
Input
Homework
LEFT side