Probability · Year 9

In Year 9 you learn: relative frequency.

Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain). You can work it out from equally likely outcomes. Or you can estimate it from an experiment, using relative frequency.

Key facts

  • P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
  • P(not A) = 1 − P(A).
  • The probabilities of all the possible outcomes add up to 1.
  • Expected frequency = probability × number of trials.
  • Relative frequency = number of times it happened ÷ number of trials. More trials give a better estimate.

Worked examples

Example 1

A playlist has 8 pop songs, 5 rock songs and 2 jazz songs, played on shuffle. Find P(rock) and P(not jazz) for the first song.

Answer: P(rock) = 1/3, P(not jazz) = 13/15

Example 2

A bus is early with probability 0.15 and on time with probability 0.6. Find P(late), and how many late days to expect in 40 school days.

Answer: 0.25; 10 days

Example 3

Two fair dice are rolled and the scores added. Find the probability of a total of 8.

Answer: 5/36

Other years