Probability: combined, conditional and independent events

Learning objectives

Use the language of trials, outcomes, equally likely outcomes, relative frequency, sample space and events, calculate P(A) = n(A)/n(U), and find the expected number of occurrences of an event

Calculate probabilities of combined events using Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes, and apply P(A ∪ B) = P(A) + P(B) − P(A ∩ B) and the complement rule

Identify mutually exclusive events (P(A ∩ B) = 0) and independent events (P(A ∩ B) = P(A)P(B)), and test for independence using P(A|B) = P(A) = P(A|B′)

Calculate conditional probabilities with P(A|B) = P(A ∩ B)/P(B) and from Venn diagrams, tree diagrams and two-way tables, including sampling with and without replacement

(HL) Apply Bayes' theorem for up to three events to reverse a conditional probability, for example in medical testing or quality control problems