Odds and Probability

Odds and Probability: In mathematical concepts, we use odds and probability calculations in many ways like while solving the Playing Cards Probability and calculating the problems like the trains may be late, it may take an hour, to reach home and so forth. Here we will be discussing Odds & Probability Topic. The definitions for both are given in this article.

However, Probability is not similar to odds, as it describes the probability that the event will occur, upon the probability that the event will not occur. So, have a look at the difference between odds and probability provided below. Also, Go through the given solved examples based on Odds and Probability to learn the concept better.

What is the Definition of Odds?

The definition of Odds in the probability of a particular event is the ratio between the number of favorable outcomes of an event to the number of unfavorable outcomes.

In short, odds are defined as the probability that a particular event will occur or not. The range of Odds is from zero to infinity, if the odds is 0, the event is not likely to occur, but if it is ∞, then it is more likely to occur.

What is the Definition of Probability?

In mathematics, the probability is the likelihood of an event or more than one event happening. It denotes the chances of obtaining certain outcomes and can be calculated with the help of simple formula. Also, you can calculate the probability with multiple events by breaking down each probability into separate single considerations and then multiplying each output together to achieve a single likely result. Probabilities constantly range between 0 and 1.

In case, odds are declared as an A to B, the chance of winning then the winning probability can be PW = A / (A + B) while the losing probability is PL = B / (A + B).

Comparison Chart of Odds and Probability

Here is the table of comparison chart to learn about odds and probability basics:

Basis for Comparison Odds Probability
Meaning Odds refers to the possibilities in favor of the event to the chances against it. Probability refers to the likelihood of occurrence of an event.
Expressed in Ratio Percent or decimal
Lies between 0 to ∞ 0 to 1
Formula Occurrence/Non-occurrence Occurrence/Whole

Key Difference Between Odds & Probabilities

The key difference between odds and probability are explained here in a simple manner to understand and learn the concepts easily and quickly:

  • The term Odds is utilized to outline that if there are any possibilities of the occurrence of an event or not. Whereas the term ‘probability’ is defined as the possibility of the happening of an event, ie., how frequently the event will happen.
  • Commonly, Odds range from zero to infinity, where zero represents the impossibility of happening of an event, and infinity signifies the possibility of the event. In contrast, probability lies between zero to one. Therefore, the closer the probability to zero, the more are the possibilities of its non-occurrence, and the closer it is to one, the higher are the possibilities of the event.
  • Odds are the ratio of positive events to negative events. However, the probability can be measured by dividing the favorable event by the overall number of events.

Solved Examples on Odds & Probability

1. What is the difference between odds and probability?


The difference between odds and probability is as illustrated below:

‘Odds’ of an event are the ratio of success to failure.

Hence, Odds = \(\frac { Success}{ Failures} \)

The ratio of the success to the amount of success and failures is known as the ‘Probability’ of an event.

Therefore, Probability = \(\frac { Success}{ (Success + Failures) } \)

2. A coin is thrown 3 times. What is the probability that at least one tail is taken?


Let’s consider the sample space for a better understanding of the possibilities

Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]

Total number of ways = 2 × 2 × 2 = 8.

Possible Cases for Tail = 7

P (A) = \(\frac { 7 }{ 8 } \)


Probability (of getting at least one tail) = 1 – P (no tail)⇒ 1 – (\(\frac { 1 }{ 8 } \)) = \(\frac { 7 }{ 8 } \)

FAQs on Odds Vs Probability

1. How do you convert odds to probability?

For converting odds to probability, we have to divide the odds by 1 + odds. For instance, let’s convert odds of 1/9 to a probability. Now, divide 1/9  by 10/9 to get the probability of 0.10.

2. What are the odds in favor?

The Odds in favor of an event equal to the number of favorable outcomes by the number of unfavorable outcomes.

P(A) = \(\frac { Number of favorable outcomes }{  Number of unfavorable outcomes } \)

3. What is the formula for odds against?

Odds against the probability formula is,

P(A) = \(\frac { Number of unfavorable outcomes }{ Number of favorable outcomes } \)

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