Back to National 4

Topic

Probability

Probability describes chance. It can be written in words, fractions, decimals, or percentages depending on the context.

Topic explanation

If 3 out of 10 counters are red, the probability of picking red is 310.

Probabilities always sit between 0 and 1. They can also be described using words like unlikely, even chance, likely, and certain.

Expected frequency gives an estimate for repeated trials. It is not a promise, but it helps make a sensible prediction.

Quick methods

Probability fraction
Use favourable outcomes over total outcomes.
Impossible
A probability of 0 means it cannot happen.
Certain
A probability of 1 means it must happen.
Expected frequency
Multiply the probability by the number of trials.

Worked examples

Example 1

A bag has 2 red counters and 3 blue counters. What is the probability of picking a red counter?

  1. There are 2 red counters.
  2. There are 2 + 3 = 5 counters in total
  3. Probability = red counters divided by total counters

So: The probability is 25.

Example 2

A fair spinner has 8 equal sections. 3 sections are green. What is the probability of landing on green?

  1. There are 3 green sections.
  2. There are 8 equal sections altogether.
  3. Use favourable outcomes over total outcomes.

So: The probability is 38.

Example 3

The probability that a train is late is 0.2. In 50 journeys, how many late trains would you expect?

  1. Expected frequency means probability multiplied by number of trials.
  2. Multiply 0.2 by 50.
  3. 0.2 × 50 = 10

So: You would expect about 10 late trains.

Practise this topicTake quiz