Grade 10 Probability

Grade 10 probability: relative frequency, Venn diagrams, mutually exclusive and complementary events, and the addition rule, with worked CAPS examples.

Probability is about 15 marks of Grade 10 Paper 1. You compare relative frequency (from an experiment) with theoretical probability, and you use Venn diagrams to organise events and to work out probabilities of 'A or B' and 'A and B'.

The key ideas are mutually exclusive events (which can't happen together), complementary events (which together cover every outcome) and the addition rule P(A or B) = P(A) + P(B) − P(A and B). Grade 11 builds on this with independent and dependent events, tree diagrams and contingency tables.

Key concepts

  • Sample space and events
  • Relative frequency versus theoretical probability
  • Venn diagrams with two events
  • Mutually exclusive events: P(A and B) = 0
  • Complementary events: P(not A) = 1 − P(A)
  • Addition rule: P(A or B) = P(A) + P(B) − P(A and B)

Worked examples

P(A) = 0.3, P(B) = 0.5 and A and B are mutually exclusive. Find P(A or B).

Mutually exclusive events can't happen together, so P(A and B) = 0 and P(A or B) = 0.3 + 0.5 = 0.8.

In a class of 30, 18 play soccer, 12 play netball and 5 play both. How many play neither?

Soccer or netball = 18 + 12 − 5 = 25. Neither = 30 − 25 = 5. On a Venn diagram: 13 soccer only, 5 both, 7 netball only, 5 outside.

The probability of rain tomorrow is 0.35. What is the probability that it does not rain?

These are complementary events: P(no rain) = 1 − 0.35 = 0.65.

A coin is tossed 50 times and lands on heads 28 times. Compare the relative frequency of heads with the theoretical probability.

Relative frequency = 28 ÷ 50 = 0.56. The theoretical probability of heads is 0.5. The two get closer as the number of tosses increases.

Common mistakes

  • Adding P(A) and P(B) for events that overlap, without subtracting P(A and B).
  • Putting the total of a set in the 'only' region of a Venn diagram.
  • Giving a probability bigger than 1.
  • Confusing mutually exclusive with complementary.

Exam tips

  • Fill in a Venn diagram from the middle (A and B) outwards.
  • Check that all the regions of your Venn diagram add up to the total.
  • Write probabilities as fractions, decimals or percentages, as the question asks.

Frequently asked questions

What does mutually exclusive mean?

Two events are mutually exclusive if they can't happen at the same time, such as rolling a 2 and a 5 on one throw of a die. Then P(A and B) = 0.

What is relative frequency?

The number of times an event happened in an experiment divided by the number of trials. With many trials it gets close to the theoretical probability.

Are tree diagrams in Grade 10?

Grade 10 focuses on Venn diagrams. Tree diagrams and contingency tables are used for independent and dependent events in Grade 11.

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