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Suppose a number, $x$, is picked randomly from the interval $[0,1]$. What is the probability that $x=1/10$? What is the probability that $x=m/10$ for some $m=0,....,10$. What is the probability that $x=m/100$ for some $m=0,...,100$? What is the probability that $x=m/n$ for some $m \le n$? What is the probability that x is rational?

Not sure how to do this. I know with an increasing sequence, the probabilities of $P(A_n)$ grow with $n$ and approach the union and with a decreasing sequence the probabilities of $P(A_n)$ get smaller with $n$ and approach the intersection. How is this useful in the given problem?

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    This doesn't make sense. The probability of $x$ being any particular number on the interval is $0$.2012-11-19
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    @Eric Angle-Why is the probability 0? If the number is on the interval, then shouldnt there be some chance it will occur?2012-11-19
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    [Eric Angle](http://en.wikipedia.org/wiki/Eric_Angle) is right; read my answer. Note the p.s. at the bottom.2012-11-19

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