6th Grade Math Textbook, Fundamentals

 &KDSWHU

12-5

Key Concept

Odds



odds against an eventnumber of unfavorable outcomesnumber of favorable outcomes

number of favorable outcomes

odds in favor of an event number of unfavorable outcomes

Odds and Fairness

Objective To compute odds in favor and odds against •To distinguish between the

two forms of odds and the language of probability • To identify fair and unfair games

Odds are another way of expressing the likelihood of an event.

Odds in favor of an event are represented by a ratio that compares

the number of favorable outcomes to the number of unfavorable

outcomes. are any outcomes that are not

represented by the event. They are the complement of the event.

Unfavorable outcomes are calculated by subtracting the number

of favorable outcomes from the total number of possible outcomes.

Unfavorable outcomes

Think

If the odds in favor of an event

are represented by the ratio a : b,

then the odds against that event

are represented by the ratio b : a.

To find the odds in favor of and against the spinner landing

on a multiple of 3, write a list of the possible outcomes.

Count the number of favorable outcomes. Then subtract

to find the number of unfavorable outcomes.

number of possible outcomes: 6 {3, 5, 21, 13, 12, 39}

number of favorable outcomes: 4 {3, 21, 12, 39}

number of unfavorable outcomes: 2 number of possible outcomes number of favorable outcomes

• Calculate the odds in favor of the event by writing the ratio of favorable
  to unfavorable outcomes. Write each ratio in simplest form, if necessary.

Odds in favor of a multiple of 3 

or 2 : 1 or 2 to 1

The odds in favor of the spinner landing on a multiple of 3 are 2 to 1.

• Calculate the odds against the event happening by writing a ratio
  of unfavorable outcomes to favorable outcomes.

Odds against a multiple of 3 

or 1 : 2 or 1 to 2

The odds against the spinner landing on a multiple of 3 are 1 to 2.

Note that when odds in favor of an event happening are 2 : 1,

there are a total of 3 possible outcomes with 2 favorable outcomes

and 1 unfavorable outcome. In this case, the probability of the event

is. So odds of 2 : 1 are the same as a probability of.^2323

1

2

2

4

number of unfavorable outcomes

number of favorable outcomes

2

1

4

2

number of favorable outcomes

number of unfavorable outcomes

3

5

21

12

39

13

Odds are commonly

expressed as a ratio a : b,

where b0; but they

may also be expressed in

fractional, decimal, or

percent form.