Year 10: Probability of simple events

A simple event is the most direct kind of probability question. There is one experiment, one event, and usually a clear set of equally likely outcomes. This is the core skill behind many Year 10 probability questions in Australia.

For equally likely outcomes,

\Pr (event) = favourable outcomes / total outcomes

When can you use the basic formula?

The basic probability fraction works when each outcome in the sample space is equally likely. That is true for fair coins, fair dice, and well-mixed selections from a set.

Example 1: What is the probability of rolling a 5 on a fair die?

Total outcomes = $6$ .
Favourable outcomes = $1$ .
$\Pr (5) = 1 / 6$ .

Working with sets of favourable outcomes

Sometimes the event includes more than one favourable outcome, even though the question is still a simple event question.

Example 2: What is the probability of rolling an even number on a fair die?

Favourable outcomes are $2, 4, 6$ .
So there are $3$ favourable outcomes out of $6$ .
$\Pr (even) = 3 / 6 = 1 / 2$ .

Probability from a collection of objects

Year 10 questions often involve choosing one item from a bag, deck, or group. The logic is the same: count the favourable items and divide by the total number of items.

Example 3: A bag contains 3 red counters, 5 blue counters, and 2 green counters. One counter is chosen at random. Find the probability of choosing a blue counter.

Total counters = $3 + 5 + 2 = 10$ .
Blue counters = $5$ .
$\Pr (blue) = 5 / 10 = 1 / 2$ .

Writing answers well

In Australian school assessments, it is good practice to simplify the fraction where possible and, if needed, also give a decimal or percentage depending on the question wording.

Example 4: If

\Pr (event) = 3 / 10

, then as a decimal it is

0.3

and as a percentage it is

30 %

Common mistakes

Using the favourable count but forgetting the total count.
Not checking whether the outcomes are equally likely.
Counting the wrong event, such as red instead of not red.
Leaving the answer unsimplified when a simpler fraction is expected.

Study routine

State the sample space first, then circle the favourable outcomes. Only after that should you write the probability fraction. This keeps the method consistent and makes mistakes easier to spot.

Skills to practise

Probability of simple events