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 outcomesFor 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 outcomesFor 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 outcomesGiven 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.
successProbability of an event is the ratio of the success to the sum of success and failure.
successProbability
Probability of Tossing Two Coins
Probability of Tossing Three Coins
Probability for Rolling Two Dice
Probability for Rolling Three Dice
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