Probability, Venn diagrams, tree diagrams and conditional probability

Learning objectives

Use the language of trials, outcomes, equally likely outcomes, sample space and events, and calculate P(A) = n(A)/n(U) for equally likely outcomes

Use the complement rule P(A′) = 1 − P(A), and calculate the expected number of occurrences of an event in n trials as nP(A)

Represent a situation with a Venn diagram, a tree diagram, a sample space diagram or a table of outcomes, and read probabilities from the representation

Apply the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and recognise mutually exclusive events as the case P(A ∩ B) = 0

Calculate a conditional probability using P(A | B) = P(A ∩ B)/P(B), and work along the branches of a tree diagram for sampling with and without replacement

Test whether two events are independent by checking whether P(A ∩ B) = P(A)P(B), and explain the difference between independent and mutually exclusive events