Display the outcomes in a three event karnaugh map

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Unformatted text preview: nd three are blue. Someone selects two at random, all possibilities being equally likely. What is the probability the two socks are the same color? Also, if instead, three socks were selected, what is the probability that at least two of them are the same color? Solution For the first question, we could imagine the socks are numbered one through nine, with socks numbered one through six being orange and and socks numbered seven through nine being blue. Let Ω be the set of all subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} of size two. The number of elements · of Ω is given by |Ω| = 9 = 928 = 36. The number of ways two orange socks could be chosen is 2 3 6 2 = 15, and the number of ways two blue socks could be chosen is 2 = 3. Thus, the probability 15+3 two socks chosen at random have the same color is 36 = 1/2. The second question is trivial. Whatever set of three socks is selected, at least two of them are the same color. So the answer to the second question is one. Example 1.4.2 Let an experiment consi...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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