In this topic, you will practice calculating the probability of multiple events. The probability of multiple events happening is the product of the probabilities of each individual event happening.

It is also useful to know the following equation

Example 1:
Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.

Probability: Odds:

Solve for the probability

P(selecting 3 highlighted pieces)	=	P(selecting highlighted piece from shape1) × P(selecting highlighted piece from shape2) × P(selecting highlighted piece from shape3)
	=	× ×
	=	× ×
	=

Solve for the odds

Odds that at least one selected piece will be unhighlighted =

Number of outcomes where at least one piece is unhighlighted

:

Number of outcomes where all selected pieces are highlighted

We will solve for the first part of the ratio by using the definition of probability:

P(at least one piece is unhighlighted)	=	1 - P(all selected pieces are highlighted)
	=	1 -	previously solved probability
	=		definition of probability

Now we know the first part of the ratio:

Number of outcomes where at least one piece is unhighlighted = 19

To find the second part of the ratio

Number of outcomes where all selected pieces are highlighted = Total number of outcomes - Number of outcomes where at least one piece is unhighlighted Therefore,
Number of outcomes where all selected pieces are highlighted = 21 - 19 = 2

So the odds that at least one selected piece will be unhighlighted is 19:2

The answer is Probability: 2 21   Odds: 19:2