Transcript A2H Ch 12 sec 4 5 Multiplying and Adding - VHS-PreCal

Chapter 12 Sec 4
Multiplying
Probability
Algebra 2 Chapter 12 Sections 4 & 5
Independent Events
• In situations with two independent events,
you can find the probability of both events
occurring if you know the probability of
each event occurring.
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Algebra 2 Chapter 12 Sections 4 & 5
Example 1
Sammie Jo has 9 dimes and 7 pennies in her pocket. She
randomly selects one coin, looks at it, and replaces it.
She then selects another coin. What is the probability
that both coins are dimes?
Find the probability of each event. Seeing as both
event are independent and the same…
d
9
9
Pd  


dp
9  7 16
To pull two dimes
9 9
81
 
16 16 256
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Algebra 2 Chapter 12 Sections 4 & 5
Example 2
When three dice are rolled, what is the probability
that two dice show 5 and the third die shows an
even number?
1
1
2. P5 
1. P5 
6
6
3 1
3. Peven   
6 2
1 1 1 1
P1, 2, and 3    
6 6 2 72
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Algebra 2 Chapter 12 Sections 4 & 5
Probability of Dependent Events
• As with two independent events, you need
to find the probability of both events
occurring if you know the probability of
each event occurring.
• The second and subsequent events will be
affected by each previous event.
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Algebra 2 Chapter 12 Sections 4 & 5
Example 1
Stephen is drawing chips from a bag to determine the
prizes to give. Of the 20 chips, 11 say computer, 8 say
trip, and 1 says car. Drawing at random and without
replacement , find the following probabilities.
1
a. A computer and a car.
11
Pcar  
PC  
19
20
11 1
11
PC then car    
or about 0.03
20 19 380
b. Two trips
8 2
PT1  

20 5
7
PT2  
19
2 7 14
PT1 then T2     or about 0.15
5 19 95
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Chapter 12 Sec 5
Adding Probability
Algebra 2 Chapter 12 Sections 4 & 5
Mutually Exclusive Events
• When you roll a die, an event such as rolling a 1 is
called a simple event because it consists of only one
event.
• An event that consists of two or more events is a
compound event.
• When the two events not related such as rolling an even
number or a 5. Since the roll can not be both the 5 and
even, these are called mutually exclusive events.
• The probability of these events are found by adding
their individual probabilities.
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Algebra 2 Chapter 12 Sections 4 & 5
Probability of Mutually Exclusive Events
Jacob has a stack of cards consisting of 10 hearts, 8
spades, and 7 clubs. If he selects a card at random, what
is the probability that it is a heart or a club?
10
7
Ph   , Pc  
25
25
10 7 17
Ph or c   

25 25 25
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Algebra 2 Chapter 12 Sections 4 & 5
Example 2
Zoe made a list of 9 comedies and 5 adventure movies she
wanted to see. She plans to select 4 titles at random to
watch this weekend. What is the probability that at least
two of the films selected are comedies?
The term at least implies 2, 3, or 4 films could be
comedies. SO, P(2) + P(3) + P(4)
C 9,2  C 5,2 C 9,3  C 5,1 C 9,4
Pat least 2 


C 14,4
C 14,4
C 14,4
360 420 126 906
Pat least 2 



 .91
1001 1001 1001 1001
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Algebra 2 Chapter 12 Sections 4 & 5
Inclusive Events
What is the probability of drawing a queen or a
diamond from a deck of cards? Since it is possible
to draw the queen of diamonds, these events are not
mutually exclusive, they are inclusive events.
4
13
1
Pq   , Pd   , Pq of d  
52
52
52
4 13 1 16
4
Pq or d     
or
52 52 52 52 13
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Algebra 2 Chapter 12 Sections 4 & 5
Example 3
There are 2400 subscribers to an Internet service
provider. Of these, 1200 own Brand A computers and
500 own Brand B computers, and 100 own both A and B.
What is the probability that a subscriber selected at
random owns either Brand A or Brand B?
1200
500
100
P  A 
, P B  
, P A and B  
2400
2400
2400
1200 500 100


P A or B  
2400 2400 2400
1600 2


2400 3
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Algebra 2 Chapter 12 Sections 4 & 5
Daily Assignment
•
Chapter 12 Sections 4 & 5
•
Study Guide (SG)
•
•
Pg 163 – 166 All
CEOC Performance Worksheet
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