UNIT OVERVIEW

Probability is the branch of mathematics that measures how likely events are to happen. You have met basic probability before. In this unit, you will build on that foundation and learn powerful new tools: Venn diagrams, the addition rule, and complementary events.

By the end of this unit, you will be able to:

• Compare experimental (relative frequency) results with theoretical probability
• Construct and interpret Venn diagrams to solve probability problems
• Apply the addition rule: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$
• Identify mutually exclusive events and know that $P(A \text{ and } B) = 0$ for them
• Work with complementary events using $P(\text{not } A) = 1 - P(A)$
• Solve multi-step probability problems with confidence

Where probability is used:

• Medical testing: Doctors interpret test accuracy using complementary events.
• Insurance: Companies calculate premiums by analysing overlapping risk factors.
• Weather forecasting: Predictions combine historical data with atmospheric models.
• Sport: Analysts use probability to guide match strategies.
• Quality control: Factories monitor defect rates to maintain standards.

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