Paper 3 · Module
Probability
Combined events and Venn diagrams
Probability starts with counting equally likely outcomes. A sample space lists them; a Venn diagram shows how events overlap; and the addition rule stops the overlap being counted twice.
≈ 30 minTree diagrams and conditional probability
Multiply along the branches, add between branches. "Given that" shrinks the sample space to the outcomes you know have happened, and does the shrinking.
≈ 40 minIndependent and mutually exclusive events
Two ideas that are easy to mix up. Mutually exclusive events cannot happen together, so their probabilities add. Independent events do not affect each other, so their probabilities multiply.
≈ 30 min