The Venn diagram shows the probabilities associated with three events XXX, Y Y\,Y and ZZZ, representing students choosing to study different languages. The probability of students studying only X X\,X is 0.15, only Y Y\,Y is 0.2, and only Z Z\,Z is 0.4. The intersection X∩Y X \cap Y\,X∩Y is q q\,q and Y∩Z Y \cap Z\,Y∩Z is ppp. Events X X\,X and Z Z\,Z are disjoint. The probability of studying none of these languages is rrr.
Write down the two events that are mutually exclusive.
Given that P(Y∣Z)=0.2P(Y | Z) = 0.2P(Y∣Z)=0.2, find the value of ppp.
Given also that X X\,X and Y Y\,Y 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.