Conditional probability - tree diagrams and the multiplication law

The multiplication of probabilities can be represented on a tree diagram.

Consider the example of the employee chosen at random:

Points to note:

• The second set of probabilities are conditional probabilities.
• The sum of the calculated probabilities is 1.

Different paths through a tree diagram represent mutually exclusive events for which the addition law for mutually exclusive events can be used.
 

If X and Y are mutually exclusive events:

Suppose two balls are removed from a bag containing three green and two red balls and that the first ball is not replaced before the second is removed. What is the probability that the balls are the same colour?

The addition law for mutually exclusive events can then be used.