AC9M10P01Year 10ProbabilityPractised on site

AC9M10P01 — Year 10 Probability

Official Curriculum Content Description:

use the language of “if ... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability

Worked Examples (1)

Example 1Independent Events Multiplication Rule

Two independent events

A

and

B

have probabilities

P(A) = \frac{5}{6}

and

P(B) = \frac{7}{12}

. Find the probability that BOTH event

A

AND event

B

occur,

P(A \text{ and } B)

. Express your answer as a fraction. (Lowest terms are not required.)

Common mistake: Adding the probabilities (applying the OR rule:

\frac{17}{12}

) instead of multiplying them for independent events.

Correct Answer:

35/72

Accepted: Any equivalent fraction is correct (for example, 105/216).

Worked Solution:

For independent events, use the AND rule (multiply probabilities):

P(A \text{ and } B) = P(A) \times P(B) = \frac{5}{6} \times \frac{7}{12} = \frac{35}{72}

Work through unlimited interactive questions for this curriculum skill, with instant answers and step-by-step methods.