A corner shop owner wants to decide whether to expand the range of energy drinks, set \(E\), or the range of magazines, set \(M\). In a survey of 80 custome...
Question 1 Report
A corner shop owner wants to decide whether to expand the range of energy drinks, set \(E\), or the range of magazines, set \(M\). In a survey of 80 customers, \(n(E) = 34\), \(n(M) = 29\), and \(n(E \cap M) = 11\).
- Work out \(n(E \cup M)\). (2)
- Work out the number of customers who buy neither product. (2)
- The owner will expand whichever category is bought by more customers who buy only that category, not both. Determine, with working, which category should be expanded. (2)
Answer Details
The inclusion-exclusion rule, \(n(E\cup M)=n(E)+n(M)-n(E\cap M)\), finds how many customers buy either product; the region outside both circles is then whatever remains of the 80 customers surveyed.
(a) \(n(E\cup M) = 34+29-11 = 52\). [2 marks]
(b) Customers buying neither product are those outside both circles: \(80-52 = 28\). [2 marks]
(c) Customers buying only energy drinks: \(34-11=23\). Customers buying only magazines: \(29-11=18\). Since \(23\gt18\), more customers buy energy drinks exclusively, so the owner should expand the energy drinks range. [2 marks]
Download The App On Google Playstore
Everything you need to excel in your exams
