Grade 9 Probability

Grade 9 probability: listing outcomes, calculating probabilities, two-stage experiments with tables and tree diagrams, and relative frequency, with examples.

Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain). In Grade 9 you list all the possible outcomes of an experiment, calculate probabilities as fractions, decimals or percentages, and handle two-stage experiments, such as tossing a coin and rolling a die, with tables or tree diagrams.

You also compare relative frequency (what actually happened in an experiment) with theoretical probability (what should happen). Grade 10 builds on this with Venn diagrams and the addition rule.

Key concepts

  • Probability = number of favourable outcomes ÷ total number of outcomes
  • Probabilities lie between 0 and 1
  • Listing outcomes in a table or tree diagram for two-stage experiments
  • P(not A) = 1 − P(A)
  • Relative frequency = number of times an event happened ÷ number of trials

Worked examples

A fair die is rolled. What is the probability of rolling a number greater than 4?

Only 5 and 6 are greater than 4: 2 favourable outcomes out of 6. P = 2/6 = 1/3.

A coin is tossed and a die is rolled. How many outcomes are possible?

2 coin outcomes × 6 die outcomes = 12 outcomes, such as H1, H2, …, T6.

Two coins are tossed. What is the probability of getting exactly one head?

The outcomes are HH, HT, TH and TT. Exactly one head happens twice (HT and TH), so P = 2/4 = ½.

The probability that it rains tomorrow is 0.3. What is the probability that it doesn't rain?

P(no rain) = 1 − 0.3 = 0.7.

Two dice are rolled. What is the probability that the total is 7?

A table of the two dice shows 36 outcomes. A total of 7 comes from (1; 6), (2; 5), (3; 4), (4; 3), (5; 2) and (6; 1): 6 outcomes. P = 6/36 = 1/6.

Common mistakes

  • Counting HT and TH as the same outcome.
  • Giving a probability bigger than 1.
  • Forgetting to simplify fractions such as 2/6.
  • Confusing relative frequency with theoretical probability.

Exam tips

  • List every outcome before counting the favourable ones.
  • Use a table for two dice and a tree diagram for coins.
  • Check that the probabilities of all the outcomes add up to 1.

Frequently asked questions

What is the difference between relative frequency and probability?

Probability is what we expect in theory, e.g. ½ for heads. Relative frequency is what actually happened, e.g. 27 heads in 50 tosses = 0.54. With more trials they get closer.

What does a probability of 0 mean?

The event is impossible, such as rolling a 7 on a normal die.

How do I show probability as a percentage?

Multiply the fraction or decimal by 100. For example, 1/4 = 0.25 = 25%.

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