Which of the following refers to the ratio of the number of favorable outcomes to the number of unfavorable outcomes?

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

Probability

Random Experiments

Experimental Probability

Events in Probability

Empirical Probability

Coin Toss Probability

Probability of Tossing Two Coins

Probability of Tossing Three Coins

Complimentary Events

Mutually Exclusive Events

Mutually Non-Exclusive Events

Conditional Probability

Theoretical Probability

Odds and Probability

Playing Cards Probability

Probability and Playing Cards

Probability for Rolling Two Dice

Solved Probability Problems

Probability for Rolling Three Dice

9th Grade Math

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