Math

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: