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 1 / 5.

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 5/ 1

Video Examples: Odd and Even Numbers

Solved Example on Odds

Ques: 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.]

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