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Shading one set but not the other on a Venn diagram, its number of elements from given counts, and the probability of choosing such an element

Shading one set but not the other on a Venn diagram, its number of elements from given counts, and the probability of choosing such an element

4 marks

The Venn diagram shows a universal set \(U\) and two sets \(C\) and \(D\).

  1. On the diagram, shade the region that represents \(C\cap D'\).

It is given that \(n(U)=80\), \(n(C)=36\), \(n(D)=28\) and \(n(C\cup D)=52\).

  1. Find \(n(C\cap D')\).
  2. One element of \(U\) is chosen at random. Find the probability that it belongs to \(C\cap D'\).

[4]

Solution:

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Answer:(a) the part of \(C\) outside \(D\) shaded (b) \(24\) (c) \(\dfrac{3}{10}\)

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