Suppose I have a fair, six-sided die. What is the expected number of rolls it would take me to get four distinct outcomes?
2026-02-23 15:25:01.1771860301
Expected number of rolls needed to get four distinct results
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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?