Suppose I have a fair, six-sided die. What is the expected number of rolls it would take me to get four distinct outcomes?


Use Geometric probability, this is called Coupon Collector's problem.

Mean number of rolls until the first: $\mathbf{E}X_1 = 1$

Mean number of rolls until the second: $\mathbf{E}X_2 = \frac{1}{\frac{5}{6}} = \frac{6}{5}$

Can you handle from here?

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    $\begingroup$ What about if I wanted to do 75% of the faces on an N sided dice? How would I do that? I'm assuming the answer is a function $\endgroup$ – ToedStorm May 19 at 10:40

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