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Suppose that $X$ is chosen uniformly from $\{1, 2, \dots , 100\}$ and given $X=x, \: Y$ is chosen uniformly from $\{1, 2, \dots , x\}$. Then $P(Y =30)=$
- $\frac{1}{100}$
- $\frac{1}{100} \times (\frac{1}{30}+ \dots + \frac{1}{100})$
- $\frac{1}{30}$
- $\frac{1}{100} \times (\frac{1}{1}+ \dots +\frac{1}{30})$