A brief explanation and the differences between odds and probability.
Definition of Odds:
Odds in probability of a particular event, means the ratio between the number of favorable outcomes to the number of unfavorable outcomes.
Odds in favor and odds in against – probability:
Odds in favor:
Odds in favor of a particular event are given by Number of favorable outcomes to Number of unfavorable outcomes.
Number of favorable outcomes
P(A) = Number of unfavorable outcomes
For example;
Find the odds in favor of throwing a die to get “3 dots”.
Solution:
Total number of outcomes in throwing a die = 6
Number of favorable outcomes = 1
Number of unfavorable outcomes = (6 - 1) = 5
Therefore, odds in favor of throwing a die to get “3 dots” is 1 : 5 or 1/5
Odds against:
Odds against is given by Number of unfavorable outcomes to number of favorable outcomes.
Number of unfavorable outcomes
P(A) = Number of favorable outcomes
For example;
Find the odds in against of throwing a die to get “3 dots”.
Solution:
Total number of outcomes in throwing a die = 6
Number of favorable outcomes = 1
Number of unfavorable outcomes = (6 - 1) = 5
Therefore, odds in against of throwing a die to get “3 dots” is 5 : 1 or 5/1
Then,
Probability of the event=
Number of favorable outcomes
Number of favorable outcomes + Number of unfavorable outcomes
Worked-out Problems on Odds and Probability:
1. If odds in favor of X solving a problem are 4 to 3 and odds against Y solving the same problem are 2 to 6.
Find probability for:
(i) X solving the problem
(ii) Y solving the problem
Solution:
Probability of the event =
Number of favorable outcomes
Number of favorable outcomes + Number of unfavorable outcomes
Given odds in favor of X solving a problem are 4 to 3.
Number of favorable outcomes = 4
Number of unfavorable outcomes = 3
(i) X solving the problem
P(X) = P(solving the problem) = 4/(4 + 3)
= 4/7
Given odds against Y solving the problem are 2 to 6
Number of favorable outcomes = 6
Number of unfavorable outcomes = 2
(ii) Y solving the problem
P(Y) = P(solving the problem) = 6/(2 + 6)
= 6/8
= 3/4
2. What is the difference between odds and probability?
Solution:
The difference between odds and probability are:
Odds of an event are the ratio of the success to the failure.
success
Odds = Failures
Probability of an event is the ratio of the success to the sum of success and failure.
success
Odds = (Success + Failures)
Probability
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Theoretical Probability
Odds and Probability
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9th Grade Math
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