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A box contains 4 red markers and 2 blue markers a marker is selected at random and it’s color is noted. If it is red it is replaced; otherwise it is not. a second marker is selected and it’s color is noted. If the second is blue, find the probability that the first was blue?

Feb 26, 2020

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$$P[\text{first was blue | second was blue}] = \\ \dfrac{P[\text{second was blue | first was blue}]P[\text{first was blue}]}{P[\text{second was blue}]} = \\ \dfrac{\dfrac 1 5 \dfrac 1 3}{\dfrac 1 5 \dfrac 1 3 + \dfrac 1 3 \dfrac 2 3} = \dfrac{\dfrac{1}{15}}{\dfrac{13}{45} }= \dfrac {3}{13}$$

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Feb 26, 2020