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**Probability**

An **event **is defined as an outcome of an experiment. The collection of all outcomes of an experiment is called a **sample space**. The probability of an event is a number between 0 and 1. If the probability of an event is zero the event is called an** impossible event. **The probability of an event is a fraction given by:

**Example: **We roll a fair die once. What is the probability of rolling a two?

##### First, we write the sample space for this experiment:

##### The number of two's in this sample space is one, therefore:

**Example: **In an experiment we roll a fair die. What is the probability of rolling an odd number?

##### The sample space is given by:

##### there are three odd numbers in the sample space: . Therefore, the probability of rolling an odd number is:

**Complimentary Events**

##### Two events **A **and **A'** are called **complementary events** if they satisfy the following equation:

**Example: **In an experiment, we roll a fair die. What is the probability of rolling a 3? What is the probability of the complement of the event rolling a 3?

##### The sample space for this question is: . There is only one 3 in the sample space, therefore, the probability of rolling a 3 is:

##### Complement of rolling a 3 is: not rolling a 3 with the following probability:

**Odds**

##### Odds in favour of an event **A** is defined as:

**Example: **What are the odds in favour of rolling an even number on a fair die?

##### The even outcomes for this experiment are: 2, 4 and 6. Therefore, we get: