# State the Probability of an Event as Odds

The probabilities can also be stated in terms of odds. For example, odds for an event or odds against an event.

Let’s say that the probability of an event occurring is P(E). If we roll a die, the probability of getting a 5 is P(5) = 1/6.

**Odds for E**

The odds for Event E to occur can be stated as follows:

In our example, the odds for getting a 5 are (1/6)/(1 – 1/6)= 1/5 or one-to-five.

**Odds against E**

The odds against Event E to occur can be stated as follows:

In our example, the odds against getting a 5 are (1 – 1/6)/(1/6)= 5/1 or 5-to-one.

The concept of odds doesn’t have much relevance in finance and investments. It is more commonly used in betting.

LESSONS

- Probability - Basic Terminology
- Two Defining Properties of Probability
- Empirical, Subjective and Priori Probability
- State the Probability of an Event as Odds
- Unconditional and Conditional Probabilities
- Multiplication, Addition and Total Probability Rules
- Joint Probability of Two Events
- Probability of Atleast One of the Events Occuring
- Dependent Vs. Independent Events in Probability
- Joint Probability of a Number of Independent Events
- Unconditional Probability Using Total Probability Rule
- Expected Value of Investments
- Calculating Variance and Standard Deviation of Stock Returns
- Conditional Expected Values
- Calculating Covariance and Correlation
- Expected Value of a Portfolio
- Variance and Standard Deviation of a Portfolio
- Bayes’ Theorem
- Multiplication Rule of Counting
- Permutation and Combination Formula

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