**Definition of Odds**

- Odds is the ratio that compares the number of favorable outcomes of an event to the number of unfavorable outcomes.

**More about Odds**

**Odds in Favor:**Odds in favor of an event = number of favorable outcomes : number of unfavorable outcomes.

For example, the odds in favor of rolling a 2 on a fair six-sided die are 1 : 5 or .

**Odds against:**Odds against an event = number of unfavorable outcomes : number of favorable outcomes.

For example, the odds against rolling a 2 on a fair six-sided die are 5 : 1 or .

**Solved Example on Odds**

Find the odds in favor of getting exactly 1 head when three coins are tossed.

Choices:

A. 3 : 5

B. 5 : 3

C. 2 : 1

D. 1 : 2

Correct answer: A

Solution:

Step 1:Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}.

Step 2:The odds in favor of getting exactly 1 head are 3 : 5. [Three outcomes are successes and 5 are failures.]

**Related Terms for Odds**

- Success
- Failures
- Probability
- Ratio
- Outcome