Odds and Probability

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)