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Topic

Probability

Probability describes chance in practical situations such as games, risk, surveys, spinners, counters, tables, and predictions.

Topic explanation

Probabilities can be written as fractions, decimals, or percentages. They must be between 0 and 1 when written as decimals.

Check whether the question asks for the event or for it not happening. P(not event) is the complement of P(event).

Frequency-table questions need the table total as the denominator. Do not use just one row or one column unless the question asks for a conditional group.

Combined probability asks for more than one event to happen. Check whether the events are independent before multiplying.

Expected frequency is an estimate for many repeated trials. It supports a sensible prediction, not a guaranteed result.

Quick methods

Simple probability
Successful outcomes over total outcomes.
Not happening
Subtract the probability from 1.
Probability scale
0 means impossible, 0.5 means even chance, and 1 means certain.
Tables
Use the correct category total over the table total.
Combined events
Multiply probabilities for independent events.
Expected frequency
Probability × number of trials

Worked examples

One event

A bag has 4 red counters, 5 blue counters and 3 green counters. What is the probability of choosing a blue counter?

  1. There are 5 blue counters.
  2. There are 4 + 5 + 3 = 12 counters in total
  3. P(blue) = 512

Answer: The probability is 512.

Watch out: Use the total number of counters as the denominator.

Not happening

A spinner has 10 equal sections. 3 are red. Find the probability of not landing on red.

  1. Sections that are not red: 10 − 3 = 7
  2. P(not red) = 710
  3. 710 = 0.7

So: The probability of not red is 710 or 0.7.

Watch out: Watch out for 310. That is the probability of red

Expected frequency

A game has a 20% chance of winning. 150 people play. Estimate how many people will win.

  1. 20% = 0.20
  2. Expected frequency = probability × number of trials
  3. 0.20 × 150 = 30

Final step: About 30 people would be expected to win.

Watch out: Expected frequency is an estimate, not a guarantee.

Probability from a table

A table shows 18 pupils chose football, 12 chose swimming, 10 chose athletics and 8 chose cycling. What is P(swimming)?

  1. Total pupils = 18 + 12 + 10 + 8 = 48
  2. Swimming pupils = 12
  3. P(swimming) = 1248 = 14

Answer: The probability is 1248, which simplifies to 14.

Watch out: The denominator is the table total, not just one row you noticed first.

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