Concept

Probability is the likelihood that an event will occur. It is written as a fraction with the number of favorable outcomes as the numerator and the total number of outcomes as the denominator. A compound event is one in which there is more than one possible outcome.

Rule

Dependent events:

The outcome of one event changes the outcome of another event.
To find the probability of two dependent events:

1. Find the probability of each event. Remember to subtract 1 from the total number of events for the second event.
2. the probability of the events

Independent events:

The outcome of one event does not change the outcome of another event.
To find the probability of independent events:

1. Find the probability of each event.
2. Find the product of the individual probabilities.

Example

If a boy picks a cube from each container, what is the probability of picking a red from the first container and a yellow from the second container?

Solution

1. Find the probability of the first event.
   There is 1 red cube and a total of 6 cubes in the first container. The probability of getting a red cube is 16.

2. Find the probability of the second event. 
   There are 3 yellow cubes in the second container. There are a total of 5 cubes in the container. The probability of getting a yellow cube is 35.

3. These are independent events. What occurs in the first container does not affect what occurs in the second container. To find the probability of both events happening, multiply the probability of the first event by the probability of the second event.

   16×35=330

This can be reduced to 110.

Pre-requisite Skills

Understanding Probability (4.4.7)