Discussion
The population of Nicosia is 75% Greek and 25% Turkish. 20% of the Greeks and 10% of the Turks speak English. A visitor to the town meets someone who speaks English. What is the probability that he is a Greek ?
Answer: D
The probability is \(\frac{6}{7}\).
By Bayes' theorem, compare the two routes to meeting an English speaker:
\[ \begin{aligned} P(G \cap E) &= 0.75 \times 0.20 = 0.150 \\ P(T \cap E) &= 0.25 \times 0.10 = 0.025 \\ P(G \mid E) &= \frac{0.150}{0.175} = \frac{6}{7} \end{aligned} \]
\(\frac{1}{7}\) is the probability that the English speaker is Turkish. \(\frac{3}{7}\), \(\frac{4}{7}\) and \(\frac{5}{7}\) come from mixing up the weights, for example ignoring the population shares.
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