operations, including brackets Understanding Risk Stage 4 Stage 5 Stage 6 Stage 7 Stage 8d Stage 8n Stage 9k Stage 10n relate relative expected apply systematic calculate the apply systematic listing frequencies to listing strategies probability of strategies including use theoretical probability, record describe and independent and of the product rule for using appropriate analyse the frequency dependent counting language and the 0 - 1 of outcomes of combined events, calculate and interpret probability scale probability including using tree conditional record describe and experiments using diagrams and other probabilities through analyse the frequency of frequency trees representations, and representation using outcomes of probability enumerate sets and know the underlying expected frequencies experiments using combinations of sets assumptions with two-way tables, tables systematically, using enumerate sets and tree diagrams and construct theoretical tables, grids and Venn combinations of sets Venn diagrams. possibility spaces for diagrams systematically, using single experiments with construct theoretical tree diagrams equally likely outcomes understand that possibility spaces for and use these to combined empirical unbiased calculate theoretical experiments with samples tend probabilities equally likely towards theoretical apply the property that outcomes and use probability the probabilities of an these to calculate distributions, with exhaustive set of theoretical increasing sample outcomes sum to one probabilities size apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments Algebraic Proficiency: visualising
operations, including brackets Understanding Risk Stage 4 Stage 5 Stage 6 Stage 7 Stage 8d Stage 8n Stage 9k Stage 10n relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale record describe and analyse the frequency of outcomes of probability experiments using tables construct theoretical possibility spaces for single experiments with equally likely outcomes and use these to calculate theoretical probabilities apply the property that the probabilities of an exhaustive set of outcomes sum to one apply systematic listing strategies record describe and analyse the frequency of outcomes of probability experiments using frequency trees enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams construct theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions enumerate sets and combinations of sets systematically, using tree diagrams understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size apply systematic listing strategies including use of the product rule for counting calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams. Algebraic Proficiency: visualising