Use the probability model
These foundations support the two-step and three-step experiments developed later in Year 10.
- Complete space List every possible outcome once
- Count only equal chances Use favourable divided by total only for equally likely outcomes
- Otherwise add probabilities For an event with several outcomes, add their assigned chances
- Complement The probabilities of A and not A add to one
Worked example
A bag contains 3 red, 2 blue and 5 yellow identical-sized counters. Each counter is equally likely to be drawn. Find the probability of not yellow
- \(\displaystyle \Pr(\text{yellow})=\frac5{10}=\frac12\)Five of the ten equally likely counters are yellow
- \(\displaystyle \Pr(\text{not yellow})=1-\frac12\)Use the complement
- \(\displaystyle \Pr(\text{not yellow})=\frac12\)Alternatively count the five red or blue counters. The three colours themselves are not equally likely
Common mistakes
Difficulty levels
Questions about this topic
What is an outcome?+
One possible result of an experiment. An event can contain one, several, all or none of the possible outcomes
When may I count favourable outcomes?+
When every elementary outcome in the sample space is equally likely
Why do probabilities total one?+
Exactly one of the complete, mutually exclusive outcomes occurs on a trial
What is the complement?+
Every outcome in the sample space that is not in the event
Does 4A complete Year 10 probability?+
No. Conditional language, two-step and three-step experiments, replacement, independence and digital simulations are developed across this chapter
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 4: Probability