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Foundation - Probability

infoWhy this? We are teaching this unit so that pupils can understand and calculate probabilities in a range of representations (tables, sample spaces, Venn diagrams and tree diagrams), enabling them to interpret data, make predictions and recognise the limitations of experimental evidence

scheduleWhy now? We are teaching it now in Year 10 so that pupils build a secure foundation in probability before tackling more complex GCSE applications in Year 11, and so they can revisit and apply these skills across other maths topics during the remainder of the course

neurologyYou need to know

  • A two-way table displays the frequencies of two categorical variables and can be used to find totals and probabilities.
  • The probability of an event is calculated as the number of successful outcomes divided by the total number of possible outcomes.
  • Experimental probability is based on the results of an actual experiment, while theoretical probability is based on expected outcomes.
  • As the number of trials in an experiment increases, the experimental probability tends to get closer to the theoretical probability (the Law of Large Numbers).
  • The expected number of times an outcome will occur can be estimated by multiplying the probability of the outcome by the total number of trials.
  • The limitations of using a sample include sampling bias and the possibility that the sample may not represent the whole population.
  • A sample space diagram lists all possible outcomes of two events, often using a grid or table.
  • Probability notation includes ( P(A) ) for the probability of event A, and ( P(A | B) ), P(A') ), etc.
  • Mutually exclusive events are events that cannot happen at the same time, and for such events, ( P(A ᴜ B) = P(A) + P(B) ).
  • A Venn diagram is used to represent sets and their relationships, including intersections and unions.
  • A tree diagram is used to show all possible outcomes of a sequence of events and their associated probabilities.

rocket_launchYou must be able to

  • Copy and complete a two-way table given partial data.
  • Find probabilities of single and combined events using a two-way table.
  • Record and interpret data from a simple experiment, such as tallying results and summarising findings.
  • Estimate probability from experimental data and compare it to theoretical probability.
  • Use probability to estimate the expected number of times an outcome will occur in a given number of trials.
  • List all possible outcomes of two events using a sample space diagram.
  • Find probabilities of events using a sample space diagram.
  • Use probability notation correctly in calculations and explanations.
  • Identify mutually exclusive events and calculate their combined probabilities.
  • Copy and complete a Venn diagram given information about sets and their intersections.
  • Find probabilities of events using a Venn diagram, including unions, intersections, and complements.
  • Copy and complete a tree diagram for two-stage events.
  • Find probabilities of outcomes using a tree diagram, including the probability of combined events.


Revision Quiz

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