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.

$\mathrm{P(E)}\mathrm{ = }\frac{\mathrm{Number\; of\; desired\; outcomes}}{\mathrm{Total\; number\; of\; possible\; outcomes}}$

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. 

$\mathrm{P(E)}\mathrm{ = }\frac{\mathrm{Number\; of\; desired\; outcomes}}{\mathrm{Total\; number\; of\; possible\; outcomes}}$

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.
$\frac{\mathrm{a}}{6}$

Sarah can place 1st only once out of those 6 outcomes.
$\frac{1}{6}$

If Sarah places first, there are 5 outcomes left for Jennifer.
$\frac{\mathrm{a}}{5}$

Jennifer can place 2nd only once out of those 5 outcomes.
$\frac{1}{5}$

Multiply Sarah’s outcomes by Jennifer’s outcomes to find the probability that both of these outcomes can occur. 
$\frac{1}{6}\mathrm{ \times }\frac{1}{5}\mathrm{ = }\frac{1}{30}$

Pre-requisite Skills

Equivalent Fractions (5.10.5)

Simplifying fractions (5.10.6)

Convert between fractions, decimals and percents (6.8.2)