Discussion
Suppose 50% of the population of a village like oranges, 70% of the population like apples, and 40% like both. If a person is picked at random who likes at least one of these fruits, what is the probability that the person likes oranges?
Answer: D
The probability is 5/8.
This is a conditional probability. The share who like at least one fruit is
\[ \begin{aligned} P(O \cup A) &= 0.5 + 0.7 - 0.4 = 0.8 \\ P(O \mid O \cup A) &= \frac{P(O)}{P(O \cup A)} = \frac{0.5}{0.8} = \frac{5}{8} \end{aligned} \]
since everyone who likes oranges is in the 'at least one' group. 1/2 ignores the condition and gives the unconditional probability. 1/8 is the share who like oranges only (0.1) divided by 0.8, and 5/12 divides 0.5 by 1.2, the sum of the two percentages without removing the overlap.
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