In a country, a share, q, of the population belongs to an ethnic group we can call A. The remaining (share 1-q) belong t

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In a country, a share, q, of the population belongs to an ethnic group we can call A. The remaining (share 1-q) belong to group B.


Now assume more generally that we have n ethnic groups. The proportion of the population that belongs to group i is 𝑞𝑖 where 0 ≤𝑞𝑖≤ 1 and Σi 𝑞𝑖 = 1, i = 1, 2, 3,… n.

a.
What possible outcomes can we get if we draw two people at random?

b.
What is the probability of each of the outcomes?

c.
Show that the probability that the two people are from different ethnic groups is 𝐸 = 1 – Σi (𝑞𝑖) ˆ2