Edexcel S1 2008 June — Question 5

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2008
SessionJune
TopicPrinciple of Inclusion/Exclusion
TypeConstrained Survey to Venn Diagram

5. A person's blood group is determined by whether or not it contains any of 3 substances \(A , B\) and \(C\). A doctor surveyed 300 patients' blood and produced the table below.
Blood containsNo. of Patients
only \(C\)100
\(A\) and \(C\) but not \(B\)100
only A30
\(B\) and \(C\) but not \(A\)25
only \(B\)12
\(A , B\) and \(C\)10
\(A\) and \(B\) but not \(C\)3
  1. Draw a Venn diagram to represent this information.
  2. Find the probability that a randomly chosen patient's blood contains substance \(C\). Harry is one of the patients. Given that his blood contains substance \(A\),
  3. find the probability that his blood contains all 3 substances. Patients whose blood contains none of these substances are called universal blood donors.
  4. Find the probability that a randomly chosen patient is a universal blood donor.