Probability

Lessons on Probability

4 Part Lesson
Venn diagrams – Mutually Exclusive and Independent Events
4 Part Lesson
Probability Trees AS Statistics
4 Part Lesson
Venn diagrams and Regions
4 Part Lesson
Probabilities from Grouped Data

Prerequisite Knowledge

  • Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
  • 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

Success Criteria

  • Understand the meanings of terms used in probability;
  • Calculate probabilities of single events;
  • Identify and use sample spaces
  • Draw and interpret Venn diagrams;
  • Understand mutually exclusive and independent events and determine whether two events are independent
  • Use and understand tree diagrams

Teaching Points

  • Students may need a recap of interpolation when finding a probability from grouped data;
  • Link probability to interpreting histograms and interpolation.
  • Whilst Venn diagrams are covered at GCSE it may be necessary to recap identifying regions using set notation.
  • Students should be able to describe the terms mutually exclusive and independent using Venn diagrams.
  • While it is not required at AS it is useful to introduce the Addition Rule when discussing the union of two sets and P(A) ⨉ P(B) = P(AnB) for independent events.
  • In addition to visualising that mutually exclusive sub-sets have no overlap students should understand P(A) n P(B) = 0 and P(A) + P(B) = P(AuB) for mutually exclusive events.

Misconceptions

  • Some students confuse the terms mutually exclusive and independent, especially when using their formulae.
  • When drawing Venn diagrams some students forget to include the box for the universal set.
  • More complicated, wordy problems can often be simplified by sketching either a Venn diagram or probability tree. How

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