# Probability of Atleast One of the Events Occuring

This refers to the addition rule.

The additional rule determines the probability of atleast one of the events occuring.

**P (A or B) = P (A) + P (B) - P (A and B)**

If A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified as follows:

**P (A or B) = P (A) + P (B) for mutually exclusive events A and B.**

**Example**

An investor is contemplating buying one of the two stocks A or B. The probability P(A) that an investor will buy stock A is 0.30. The probability P(B) that the investor will buy stock B is 0.50. The probability that he may buy both P(A and B) is 0.10.

The probability that the investor will buy atleast one of the two stocks (A, or B, or both) is calculated as follows:

**P(A or B) = 0.30 + 0.50 – 0.10 = 0.70**

Suppose P(A) and P(B) are mutually exclusive events, that is, the investor will buy only one of the two stocks, then:

**P(A or B) = 0.30 + 0.50 = 0.80**

- 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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