ExplanationIn essence, the question is asking, “What is the probability that one or more days are rainy days?” since any single rainy day would mean the city experiences rain. In this case, employ the 1 – x shortcut, where the probability of rain on one or more days is equal to 1 minus the probability of no rain on any day.
Since the probability of rain is \(\frac{1}{3}\) on any given day, the probability of no rain on any given day is \(1 - \frac{1}{3}=2/3\) .
Therefore, the probability of no rain on three consecutive days is \(\frac{2}{3}\frac{2}{3}\frac{2}{3}=\frac{8}{27}\).
Finally, subtract from 1 to find the probability that it rains on one or more days: P(1 or more days) = 1 – P(no rain) = \(1 - \frac{8}{27}=\frac{19}{27}\).
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