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Probability

infoWhy this? Experimental probability, two-way tables, and sample-space diagrams allow us to organise evidence and model combinations of events systematically. Comparing observed frequencies with calculated probabilities develops informed reasoning about uncertainty.

scheduleWhy now? This unit extends Year 7 work on single events, sample spaces, and complements to empirical data and paired outcomes. These representations prepare us for Venn diagrams, tree diagrams, and reasoning about independent and mutually exclusive events.

neurologyYou need to know

  • A two-way table is a way of organising data that shows the frequency of combinations of two categorical variables.
  • The sum of all frequencies in a two-way table equals the total number of outcomes or trials.
  • When all elementary outcomes are equally likely, `P(A)` equals the number of favourable outcomes divided by the total number of possible outcomes.
  • Experimental probability is calculated using data collected from an experiment, not theoretical assumptions.
  • The expected number of times an outcome will occur is found by multiplying the probability of the outcome by the total number of trials.
  • A sample space diagram lists all possible outcomes of one or more events.
  • For two independent events, the total number of possible outcomes is the product of the number of outcomes for each event.
  • Probabilities from a sample space diagram can be found by counting the number of favourable outcomes and dividing by the total number of possible outcomes.
  • Probabilities are always between 0 and 1, inclusive.
  • The sum of probabilities for all possible outcomes in a sample space is 1.

rocket_launchYou must be able to

  • Complete a two-way table given partial data, including filling in missing totals and frequencies.
  • Use data from a two-way table to calculate probabilities of single events and combined events. Exemplification
  • Record data accurately from a simple experiment, such as coin tosses, dice rolls, or drawing coloured counters. Exemplification
  • Interpret data from a simple experiment to describe observed frequencies and patterns.
  • Estimate the probability of an event based on experimental data. Exemplification
  • Use estimated probabilities to calculate the expected number of times an outcome will occur in a given number of trials. Exemplification
  • List all possible outcomes for two events using a sample space diagram. Exemplification
  • Find and interpret probabilities of specific outcomes or combinations of outcomes using a sample space diagram. Exemplification


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