Concept

Probability tells you the likelihood of an event happening. The higher the probability, the more likely it is to happen. 

Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen.
Greatest Common Factor (GCF): the greatest factor of two or more numbers.

Rule

To figure out all the possible outcomes:  
Use the image, and/or a piece of scratch paper, to write all the possible combinations of outcomes.

To write the probability as a fraction in simplest form: 
1. Use the image, and the clues given in the problem, to write a fraction.

P(E) = Number of desired outcomesTotal number of possible outcomes

2. Simplify the fraction by dividing the numerator and denominator by the GCF (Greatest Common Factor). 

Example

Sarah and Jennifer are competing with 4 other students to get the highest grade in the class. What is the probability that Sarah will get the highest grade and Jennifer the second-highest grade?

Write your answer as a fraction in simplest form.

Solution

To write the probability as a fraction:
1. Use the clues given in the problem to write a fraction. 

P(E) = Number of desired outcomesTotal number of possible outcomes

The problem says there are 6 different students competing. That means Sarah can place in either 1st, 2nd, 3rd, 4th, 5th, or 6th place, so there are 6 different outcomes.
a6

Sarah can place 1st only once out of those 6 outcomes.
16

If Sarah places first, there are 5 outcomes left for Jennifer.
a5

Jennifer can place 2nd only once out of those 5 outcomes.
15

Multiply Sarah’s outcomes by Jennifer’s outcomes to find the probability that both of these outcomes can occur. 
16 × 15 = 130

Pre-requisite Skills

Equivalent Fractions (5.10.5)

Simplifying fractions (5.10.6)

Convert between fractions, decimals and percents (6.8.2)