Download Mutually Exclusive events

Mutually Exclusive events
Today we will…
1. Recap last week and correct homework
2. Mutually exclusive and non mutually
exclusive events
3. Use of Venn Diagrams to represent mutually
exclusive events
Mutually Exclusive Events
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2
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Consider these two events
1. Drawing a red card
2. Drawing an even Card
4
5
7
9
Mutually Exclusive Events
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2
3
4
5
7
9
These two outcomes cannot happen together because
there is no red card with an even number on it
These outcomes are said to be mutually exclusive
Mutually exclusive events
If the events A and B cannot happen together
we calculate its Probability by
P(A or B) = P(A) + P(B)
This is called the addition law
Mutually Exclusive Events
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2
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7
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P ( red card or even number) = P(red) + P(even)
= 3/7 + 2/7
= 5/7
Outcomes are mutually exclusive if they cannot happen
together
Non-Mutually Exclusive Events
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3
4
5
6
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What is the probability of a red card or an even number?
There are 3 red cards and 3 even numbers
Non-Mutually Exclusive Events
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P(red) + P(even) is not 3/7 + 3/7 because 4 is now
counted twice
When 2 events can occur at the same time
P(A or B) = P(A) + P(B) - P(A and B)
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Non-Mutually Exclusive Events
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P(Red or Even) = P(Red) + P(Even) – P(Red and Even)
= 3/7 + 3/7 – 1/7
= 5/7
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Try for yourself…
Question 5 Page 156
Use of Venn Diagrams
Sometimes it can be useful to represent these
questions in Venn Diagrams
It allows us to organize our information and
perform our calculations faster
U
The Venn Diagram shows
the sports played by
members of the Sport
Club
How many members
played
1. Both football and
Tennis
2. Tennis but not Football
3. Neither
4. Football or tennis
Calculate the Probability
of each
Football
40
Tennis
10
35
45
Homework
Question 5 and 6 Page 159