9-8 Odds
Pre-Algebra HOMEWORK
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9-8 Odds
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Pre-Algebra
9-8
9-8 Odds
Odds
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
9-8 Odds
Warm Up
A bag contains 15 nickels, 10 dimes, and 5
quarters. Two coins are drawn without
replacement.
1. Find the probability that the first is a
dime and the second is a quarter.
5
87
2. Find the probability that they are both
nickels.
7
29
Pre-Algebra
9-8 Odds
Problem of the Day
Larissa was born in August. What is the
probability that she was born on an
odd-numbered day? ≈ 0.52
Pre-Algebra
9-8 Odds
Today’s Learning Goal Assignment
Learn to convert
between
probabilities and
odds.
Pre-Algebra
9-8 Odds
Vocabulary
odds in favor
odds against
Pre-Algebra
9-8 Odds
The odds in favor of an event is the ratio of
favorable outcomes to unfavorable outcomes. The
odds against an event is the ratio of unfavorable
outcomes to favorable outcomes.
odds in favor
a:b
odds against
b:a
a = number of favorable outcomes
b = number of unfavorable outcomes
a + b = total number of outcomes
Pre-Algebra
9-8 Odds
Additional Example 1A: Estimating Odds from an
Experiment
In a club raffle, 1,000 tickets were sold, and
there were 25 winners.
A. Estimate the odds in favor of winning this
raffle.
The number of favorable outcomes is 25, and the
number of unfavorable outcomes is 1000 – 25 =
975. The odds in favor of winning this raffle are
about 25 to 975, or 1 to 39.
Pre-Algebra
9-8 Odds
Try This: Example 1A
Of the 1750 customers at an arts and crafts
show, 25 will win door prizes.
A. Estimate the odds in favor winning a door
prize.
The number of favorable outcomes is 25,
and the number of unfavorable outcomes is
1750 – 25 = 1725. The odds in favor of
winning a door prize are about 25 to 1725,
or 1 to 69.
Pre-Algebra
9-8 Odds
Additional Example 1B: Estimating Odds from an
Experiment
In a club raffle, 1,000 tickets were sold, and
there were 25 winners.
B. Estimate the odds against winning this
raffle.
The odds in favor of winning this raffle are 1
to 39, so the odds against winning this raffle
are about 39 to 1.
Pre-Algebra
9-8 Odds
Try This: Example 1B
Of the 1750 customers to an arts and crafts
show, 25 win door prizes.
B. Estimate the odds against winning a door
prize at the show.
The odds in favor of winning a door prize are
1 to 69, so the odds against winning a door
prize are about 69 to 1.
Pre-Algebra
9-8 Odds
Probability and odds are not the same thing, but
they are related. Suppose you want to know the
probability of rolling a 2 on a fair die. There is
one way to get a 2 and five ways not to get a 2,
so the odds in favor of rolling a 2 are 1:5. Notice
the sum of the numbers in the ratio is the
denominator of the probability 1 .
6
Pre-Algebra
9-8 Odds
Additional Example 2A: Converting Odds to
Probabilities
A. If the odds in favor of winning a CD player
in a school raffle are 1:49, what is the
probability of winning a CD player?
1
1
P(CD player) = 1 + 49 =
50
Pre-Algebra
On average there
is 1 win for every
49 losses, so
someone wins 1
out of every 50
times.
9-8 Odds
Try This: Example 2A
A. If the odds in favor of winning a bicycle in a
raffle are 1:75, what is the probability of
winning a bicycle?
1
1
P(bicycle) = 1 + 75 =
76
Pre-Algebra
On average there
is 1 win for every
75 losses, so
someone wins 1
out of 76 times.
9-8 Odds
Additional Example 2B: Converting Odds to
Probabilities
B. If the odds against winning the grand prize
are 11,999:1, what is the probability of
winning the grand prize?
If the odds against winning the grand prize are
11,999:1, then the odds in favor of winning the
grand prize are 1:11,999.
1
1
P(grand prize) =
=
≈ 0.000083333
1 + 11,999
12,000
Pre-Algebra
9-8 Odds
Try This: Example 2B
B. If the odds against winning the grand prize
are 19,999:1, what is the probability of
winning the grand prize?
If the odds against winning the grand prize are
19,999:1, then the odds in favor of winning the
grand prize are 1:19,999.
1
1
P(grand prize) =
=
≈ 0.00005
1 + 19,999
20,000
Pre-Algebra
9-8 Odds
1
Suppose that the probability of an event is 3 .
This means that, on average, it will happen in 1
out of every 3 trials, and it will not happen in 2
out of every 3 trials, so the odds in favor of the
event are 1:2 and the odds against the event are
2:1.
CONVERTING PROBABILITIES TO ODDS
If the probability of an event is m , then the odds
n
in favor of the event are m:(n – m) and the odds
against the event are (n – m):m.
Pre-Algebra
9-8 Odds
Additional Example 3: Converting Probabilities to
Odds
A. The probability of winning a free dinner is 1 .
20
What are the odds in favor of winning a free
dinner?
On average, 1 out of every 20 people wins, and the
other 19 people lose. The odds in favor of winning
the meal are 1:(20 – 1), or 1:19.
1 .
B. The probability of winning a door prize is 10
What are the odds against winning a door
prize?
On average, 1 out of every 10 people wins, and
the other 9 people lose. The odds against the
door prize are (10 – 1):1, or 9:1.
Pre-Algebra
9-8 Odds
Try This: Example 3
A. The probability of winning a free laptop is 1 .
30
What are the odds in favor of winning a free
laptop?
On average, 1 out of every 30 people wins, and
the other 29 people lose. The odds in favor of
winning the meal are 1:(30 – 1), or 1:29.
1 .
B. The probability of winning a math book is 50
What are the odds against winning a math
book?
On average, 1 out of every 50 people wins, and
the other 49 people lose. The odds against the
door prize are (50 – 1 ):1, or 49:1.
Pre-Algebra
9-8 Odds
Lesson Quiz
Of 200 people at the grand opening of a store,
10 will win door prizes.
1. Estimate the odds of winning a door prize. 1:19
2. Estimate the odds against winning a door prize. 19:1
3. If the odds of winning a new computer are 1:899,
what is the probability of winning the computer? 1
900
1
4. The probability of winning a new truck is 600,000 .
What are the odds against winning the truck?
599,999:1
Pre-Algebra