The Venn diagram shows three events XXX, Y Y\,Y and ZZZ. Events X X\,X and Y Y\,Y overlap, while event Z Z\,Z is separate from both of them. The probability in the region belonging to X X\,X only is 0.25, and the probability outside all three events is 0.05. The other regions are labelled as follows: X X\,X and Y Y\,Y only has probability ppp, Y Y\,Y only has probability qqq, and Z Z\,Z only has probability rrr.
Write down two of the events that are mutually exclusive.
The probability of X X\,X is 0.55.
The probability of X X\,X or Y Y\,Y is 0.80.
Find the values of ppp, q q\,q and rrr.
State, giving a reason, whether or not the events X X\,X and Y Y\,Y are statistically independent.
34 exam-style questions on Edexcel AS Level Maths Probability, covering 5.1 Calculating Probabilities, 5.2 Venn Diagrams, 5.3 Mutually Exclusive and Independent Events, and 5.4 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.