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# At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given da

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At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given day, what is the probability that Joe will eat at least two different kinds of fruit?

Nov 8, 2018

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$$P[\text{Joe eats at least two different kinds of fruit}] = \\ 1-P[\text{Joe only eats 1 kind of fruit}] = \\ 1 - 3\cdot \left(\dfrac 1 3\right)^3 = \\ 1 - \dfrac 1 9 = \\ \dfrac 8 9$$

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Nov 8, 2018