- 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

# Bayes’ Theorem

Bayes’ Theorem formula, also known as Bayes’ Law, or Bayes’ Rule, is an intuitive idea. We adjust our perspective (the probability set) given new, relevant information. Formally, Bayes’ Theorem helps us move from an unconditional probability (what are the odds the economy will grow?) to a conditional probability (given new evidence, what are the odds the economy will grow?)

Suppose your daughter tells you that her friend is coming home tomorrow. Since you don’t know anything else, there is a 50% chance that the friend is a female. Now she tells you that her friend has long hair. With this additional information there are now more chances that the friend is a female. Bayes’ theorem can be applied in such scenarios to calculate the probability (probability that the friend is a female.)

A simple representation of Bayes’ formula is as follows:

**Example 1**

The following information is available regarding drug testing.

- 0.5% of people are drug users
- A test has 99% accuracy. 99% of drug users and 99% of non-drug users are correctly identified by it.

The problem question is to find the probability of being a drug user if you’ve tested positive?

The solution according to Baye’s theorem is as follows:

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