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Thursday, 4 August 2011

Math GRE - #3

A drawer contains 2 blue, 4 red, and 2 yellow socks. If 2 socks are to be randomly selected from the drawer, what is the probability that they will be the same colour?

  • $\frac{2}{7}$
  • $\frac{2}{5}$
  • $\frac{3}{7}$
  • $\frac{1}{2}$
  • $\frac{3}{5}$

    The probability of getting 2 blue in a row is: $\frac{2}{8}\frac{1}{7}=\frac{1}{28}$.

    The probability of getting 2 yellow in a row is: $\frac{2}{8}\frac{1}{7}=\frac{1}{28}$.

    The probability of getting 2 red in a row is: $\frac{4}{8}\frac{3}{7}=\frac{6}{28}$.

    So the total probability is: \[\frac{1}{28}+\frac{1}{28}+\frac{6}{28}=\frac{2}{7}.\]


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