Transcript A Survey of Mathematics with Applications

P-3 Probability
Odds
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 1
WHAT YOU WILL LEARN
• Odds against an event and odds in
favor of an event
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 2
Odds Against

Odds against event 

P event fails to occur

P event occurs



P success 


P failure
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 3
Example: Odds Against


Example: Find the odds against rolling a 5 on
one roll of a die.

1
P 5 
6


5
P fails to roll a 5 
6
5
5 6 5
odds against
6
   
rolling a 5
1 6 1 1
6
The odds against rolling a 5 are 5:1.
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 4
Odds in Favor

Odds in favor of event 

P event occurs

P success 

P failure 
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
P event fails to occur

Chapter 12 Section 3 - Slide 5
Example

Find the odds in favor of landing on blue in one
spin of the spinner.


3
P blue 
8


5
P not blue 
8
3
3 8 3
8
odds in favor    
5 8 5 5
8
The odds in favor of spinning blue are 3:5.
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 6
Probability from Odds



Example: The odds against spinning a blue on
a certain spinner are 4:3. Find the probability
that
a) a blue is spun.
b) a blue is not spun.
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Chapter 12 Section 3 - Slide 7
Solution

Since the odds are 4:3 the denominators must
be 4 + 3 = 7.

The probabilities ratios are:
3
P (blue ) =
7
4
P (not blue) =
7
Copyright © 2009 Pearson Education, Inc.
Chapter 12 Section 3 - Slide 8
Five red apples and six yellow apples are placed
in a bag. If one apple is selected at random,
determine the odds against the apple being
yellow.
a.
5:11
b.
6:11
c.
5:6
d.
6:5
Copyright © 2009 Pearson Education, Inc.
Slide 12 - 9
Five red apples and six yellow apples are placed
in a bag. If one apple is selected at random,
determine the odds against the apple being
yellow.
a.
5:11
b.
6:11
c.
5:6
d.
6:5
Copyright © 2009 Pearson Education, Inc.
Slide 12 - 10
Five red apples and six yellow apples are placed
in a bag. If one apple is selected at random,
determine the odds in favor of the apple being
red.
a.
5:11
b.
6:11
c.
5:6
d.
6:5
Copyright © 2009 Pearson Education, Inc.
Slide 12 - 11
Five red apples and six yellow apples are placed
in a bag. If one apple is selected at random,
determine the odds in favor of the apple being
red.
a.
5:11
b.
6:11
c.
5:6
d.
6:5
Copyright © 2009 Pearson Education, Inc.
Slide 12 - 12
The odds against the Blue Streaks winning the
basketball game are 7:5. What is the probability
that the Blue Streaks win the game?
a.
5
12
c.
1
5
Copyright © 2009 Pearson Education, Inc.
b.
7
12
d.
1
7
Slide 12 - 13
The odds against the Blue Streaks winning the
basketball game are 7:5. What is the probability
that the Blue Streaks win the game?
a.
5
12
c.
1
5
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b.
7
12
d.
1
7
Slide 12 - 14
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Slide 12 - 15
Copyright © 2009 Pearson Education, Inc.
Slide 12 - 16