9-8 Odds
Learn to convert between probabilities and
odds.
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
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
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
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 16.
Pre-Algebra
9-8 Odds
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
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
13
Suppose that the probability of an event is .
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
m
If the probability of an event is , then the odds in
n
favor of the event are m:(n – m) and the odds
against the event are (n – m):m.
Pre-Algebra
9-8 Odds
Example 3: Converting Probabilities to Odds
A. The probability of winning a free dinner is
odds in favor of winning a free dinner?
1the
. What are20
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.
1the
B. The probability of winning a door prize is . What are10
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
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
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 16.
Pre-Algebra
9-8 Odds
13
Suppose that the probability of an event is .
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
m
If the probability of an event is , then the odds in
n
favor of the event are m:(n – m) and the odds
against the event are (n – m):m.
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
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
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
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
Try This Together: Example 3
A. The probability of winning a free laptop is
odds in favor of winning a free laptop?
1the
. What are30
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.
1the
B. The probability of winning a math book is . What are50
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