AC9M9P02Year 9ProbabilityPractised on site

AC9M9P02 — Year 9 Probability

Official Curriculum Content Description:

calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”

Worked Examples (1)

Example 1Mutually Exclusive Addition Rule
A spinner used in a maths lesson has several coloured sections. The probability of landing on red is 316\frac{3}{16} and the probability of landing on blue is 1116\frac{11}{16}. Since landing on red and landing on blue are mutually exclusive events, what is the probability of landing on red OR blue? Express your answer as a fraction. (Lowest terms are not required.)
Common mistake: Multiplying the probabilities (applying the AND rule: 33256\frac{33}{256}) instead of adding them for mutually exclusive events.
Correct Answer:7/87/8
Accepted: Any equivalent fraction is correct (for example, 21/24).
Worked Solution:
For mutually exclusive events, use the OR rule (add probabilities): P(red or blue)=P(red)+P(blue)=316+1116=1416P(\text{red or blue}) = P(\text{red}) + P(\text{blue}) = \frac{3}{16} + \frac{11}{16} = \frac{14}{16} = 78\frac{7}{8}.

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