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There are 11 songs on a playlist, 5 are slow and 6 are fast. When the DJ plays a song it will not be played again. what is the probability that the first two songs are played slow?

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    $\begingroup$ Where is the Geometry here? $\endgroup$
    – JB King
    Jun 4, 2013 at 19:33

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For the first track, there are 11 choices of song, of which 5 are slow. Thus there’s a 5/11 probability that the first track played will be slow.

Let’s suppose the first track is a slow song. For the second track, there are now 10 choices of song, of which 4 are slow. There’s thus a 4/10 = 2/5 probability that the second track played will be slow (given that the first track was slow).

Thus, the probability that the first two tracks played are slow is given by $$\frac{5}{11} \times \frac{2}{5} = \frac{2}{11}.$$ (Although I don’t see the geometrical aspect.)

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