Suppose that n observations are chosen at random from a continuous pdf fY(y).  What is the probability that the last observation recorded will be the smallest number in the sample

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Chapter9: Solving Quadratic Functions
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Suppose that n observations are chosen at random from a continuous pdf fY(y).  What is the probability that the last observation recorded will be the smallest number in the sample?

I asked this question earlier today, but didn't quite understand all of the response.  P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?  

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