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# probability

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I have 5 red plates and 4 blue plates. If I randomly select three plates to serve dinner on, what is the probability that they're all the same color?

Dec 28, 2020

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$$P[\text{2 red plates}]=\dfrac 5 9 \dfrac 4 8 = \dfrac{5}{18}\\ P[\text{2 blue plates}] = \dfrac 4 9 \dfrac 3 8 = \dfrac{1}{6}\\ P[\text{plates are same color}]=\dfrac{5}{18}+\dfrac 1 6 = \dfrac 4 9$$

Credit to Rom; https://web2.0calc.com/members/rom/

Dec 28, 2020