🎯 Learning Objectives
- calculate expected frequency;
- estimate numbers of events in repeated trials;
- distinguish expectation from a guaranteed result;
- reverse expected-frequency calculations.
Introduction
This lesson develops Expected Frequency and Applications from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Expected Frequency
If P(red)=0.3 and a spinner is used 200 times, expected red frequency=0.3×200=60.
Interpret Carefully
Expected frequency is a long-run prediction. Exactly 60 reds are not guaranteed in one set of 200 spins.
Worked Reverse Example
An event is expected 45 times in 180 trials.
P(event)=45/180=1/4.
Practice Questions
- P(win)=0.08. Find expected wins in 500 games.
- A six is expected 120 times. Approximately how many fair die rolls are planned?
- Why might observed frequency differ from expected frequency?
✅ Check Your Work
Show answers and working
- 0.08×500=40 wins.
- (1/6)n=120, so n=720 rolls.
- Random variation causes actual trials to fluctuate around expectation.
🧪 Math Lab: Expected Frequency
Predict how often an event should occur.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.