# Probability

Students learn how to measure the likelihood of an event happening using keywords, fractions, decimals and percentages.  Learning progresses on to calculating a relative frequency and using tree diagrams to find the probability of two or more events.

This unit takes place in  and follows on from working with fractions and mixed numbers.

##### Prerequisite Knowledge
• compare and order fractions whose denominators are all multiples of the same number
• identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• add and subtract fractions with the same denominator and denominators that are multiples of the same number

##### Success Criteria
• record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
• apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
• relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale
• apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
• understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
• enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
• construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
• calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

##### Key Concepts
• Use the probability scale and associated keywords to begin comparing the likelihood of an event’s occurrence.
• When writing probabilities as a fraction using the probability scale to show equivalences with the keywords
• Discuss the effect of bias and sample size when comparing theoretical and experimental probabilities.
• Use the random function on a calculator or spreadsheet to demonstrate simple randomisation.
• When listing the outcomes of combined events ensure students use a logical and systematic method.
• Branches on a probability tree have a sum of one as they are mutually exclusive.

##### Common Misconceptions
• Writing probabilities as a ratio is a common misconception.
• When creating Venn diagrams students often forget to place the remaining events outside the circles.
• When listing permutations of combined events students often repeat events when they do not use a logical and systematic method.

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