A drawer contains 3 black socks, 4 red socks and 6 white socks. What is the probability that there is a matching pair of socks if three socks are taken from the drawer at random?
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1What do you think? What have you tried? – aduh Sep 25 '16 at 15:20
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I thought we should divide 25 by 286 but it's incorrect – Mary Sep 25 '16 at 15:22
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Hint: try finding the complement, that there are no matching socks among the three chosen. Then subtract that probability from $1$ to get your answer. – aduh Sep 25 '16 at 15:23
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Possible dublicate of http://math.stackexchange.com/questions/1915191/what-is-the-smallest-number-of-socks-you-should-pull-out-so-that-you-can-be-assu – Kaligule Sep 25 '16 at 15:29
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I think the correct answer is 137/143 but I'm not sure. Could you check if it's correct or not? – Mary Sep 25 '16 at 16:15
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The correct answer is $107/143$. See demarco's solution. – N. F. Taussig Oct 09 '16 at 17:54
1 Answers
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The easiest way to solve this is by calculating the probability of the complement and subtracting the answer from one. To calculate the probability directly would require you to count all the ways of getting at least 2 of one color. There are $\binom{13}{3}$ ways of choosing the socks and $6 \cdot 4 \cdot 3$ ways of getting a combination of three unique colors. So the answer is $$ 1-\frac{6 \cdot 4 \cdot 3}{\binom{13}{3}} $$
demarco
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