6a mutually exclusive events
Unit 2
Lesson 5
Multiple Events
Results that overlap...
Scenario: One card is randomly drawn from a deck of 52 cards. The card is face down on the table. What is the probability of getting a Jack or a Spade?
Reasoning: In a deck of card, they are 52 cards in which 4 are Jacks and 13 are Spade. So...
P(Jack or Spade) = P(Jack) + P(Spade) = Can you find the error in this reasoning?
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6a mutually exclusive events
Mutually Exclusive Events
Different events that share no outcomes in common are said to be mutually exclusive.
P( A or B ) = P(A) + P(B)
Different events that share outcomes are said to be inclusive.
P( A or B ) = P(A) + P(B) ­ P( A and B )
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6a mutually exclusive events
Classify the following events as either mutually exclusive or inclusive.
a)
The experiment is rolling a die. The 1st event: the number is greater than 3
The 2nd event: the number is even.
b)
The experiment is an activity for Saturday. The 1st event: to watch a movie
The 2nd event: to go out dancing.
c)
The experiment is answering multiple choice questions. The 1st event: the correct answer is chosen
The 2nd event: the answer A is chosen.
d)
The experiment is selecting a chocolate bar. The 1st event: the bar has nuts
The 2nd event: the bar has caramel.
Venn Diagrams
Venn Diagrams can be used to see the interaction of different events, like area models, without being drawn to scale.
B
A
1
2
3
4
Region
1
2
3
4
Description
event A only
events A and B
event B only
neither A nor B
sample space
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6a mutually exclusive events
Complete the venn diagram.
even
multiple of 5
15
5
25
10
4
8
20
2
17
7
Example1
Using the following diagram, calculate...
B
A
19
12
59
10
100
n( A or B) = n( A and B) = n( A and B) = 4
6a mutually exclusive events
Example 2 When you arrive home today, you find 27 cupcakes in a large circular plate. There are 13 that have icing 11 have sprinkles, and 4 have both.
Find...
n (icing)
n (sprinkles)
n (icing and sprinkles)
n (icing or sprinkles)
n (icing or sprinkles)
n (icing and sprinkles)
Example 3
The results of a survey on reading habits include the following:
• 85% read the newspapers
• 35% read books
• 25% read both
What is the probability that an individual :
a) reads books but not newspapers?
b) reads books or newspapers?
c) does not read books or newspapers?
5
6a mutually exclusive events
Practice 1 ++
Consider the following diagram of an experiment.
A
B
4
7
3
5
a) P(A) =
b) P(B) =
c) P(A only) =
d) P(B only) =
e) P(A or B) =
f) P(A and B) =
g) P(A or B) =
h) P(A or B) =
19
Practice 2
Consider the following diagram of an experiment.
a) Are these events mutually exclusive?
VHS
18
b) How many people were in the sample space?
DVD
0
36
7
61
c) How many own both a VHS and a DVD player?
d) How many owned neither?
6
6a mutually exclusive events
Worksheet
The dependance of events...
Scenario: Two cards are randomly drawn from a deck of 52 cards. The cards are face down on the table. What is the probability of getting two clubs?
Reasoning: In a standard deck, there are 52 cards of which 13 are clubs. So...
P(2 Clubs) = P(Club) x P(Club) = Can you find the error in this reasoning?
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6a mutually exclusive events
Independent and Dependent Events
Two events are independent if the probability that each event will occur is not affected by the occurrence of the other event. If events are not independent, then they are dependent.
The probability for independent events is:
P( A and B ) = P( A ) P( B )
Example:
1. If A and B are independent, find P(A and B)
P(A) = 0.5
P(B) = 0.7
Example 2
Classify the following events as either independent or dependent.
• rolling a 5 on a die, and flipping tails on a coin
• rolling even on a die, and rolling odd on another die
• a mother's hair is blonde, her daughter's hair is also blonde
• being dealt five spades from a standard deck of cards
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6a mutually exclusive events
Example 3
What is the probability that you will get tails when you flip a coin, and a 3 when you roll a die?
Find your answer using 3 different methods (Venn Diagram, Area Model, and the Independence Formula) '3'
Tails
5
Heads
1
1
5
T1
T2
T3
T4
T5
T6
H1
H2
H3
H4
H5
H6
12
Tails
P(Tails and 3) =P(Tails) x P(3) = Example 4 If the probability that person A will be alive in 20 years is 0.7 and the probability that person B will be alive in 20 years is 0.5, what is the probability that they will both be alive in 20 years?
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6a mutually exclusive events
Practice1
A die is tossed twice. Find the probability of getting a 4 or 5 on the first toss and a 1, 2, or 3 on the second toss.
Practice 2
A box contains 100 items of which 4 are defective. Two items are chosen at random from the box. What is the probability of selecting
(a) 2 defectives if the first item is not replaced;
(b) 2 defectives if the first item is put back before choosing the second item;
(c) 1 defective and then 1 non­defective if the first item is not replaced?
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