The events A and B are such that P(A)=0.3P(A) = 0.3P(A)=0.3 and P(A∪B)=0.7P(A \cup B) = 0.7P(A∪B)=0.7.
Verify that P(A′∩B′)=0.3P(A' \cap B') = 0.3P(A′∩B′)=0.3
Verify that P(A′∩B)=0.4P(A' \cap B) = 0.4P(A′∩B)=0.4
Given also that the events A and B are independent, verify that P(B)=4/7P(B) = 4/7P(B)=4/7
Verify that P(A′∪B′)=29/35P(A' \cup B') = 29/35P(A′∪B′)=29/35
368 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.