The Venn diagram shows the probabilities associated with three events SSS, T T\,T and UUU, representing materials found in a recycling center. The probability of a sample containing only S S\,S is 0.2, only T T\,T is 0.05, and only U U\,U is 0.25. The intersection S∩T S \cap T\,S∩T is q q\,q and T∩U T \cap U\,T∩U is ppp. There is no overlap between events S S\,S and UUU. The probability of a sample containing none of these materials is rrr.
Write down the two events that are mutually exclusive.
Given that P(T∣U)=0.5P(T | U) = 0.5P(T∣U)=0.5, find the value of ppp.
Given also that S S\,S and T T\,T are independent, find the values of q q\,q and rrr.
Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 100 questions covering Set Notation, Conditional Probability, Conditional Probabilities in Venn Diagrams, Probability Formulae, and Tree Diagrams, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.