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Jan 8 at 15:41 vote accept Benjamin Kay
Jan 8 at 2:52 comment added Ben @Henry: The coupon-collector distribution is a slightly different distribution which forms the solution to an inverse problem relating to this situation (see e.g., O'Neill 2022).
Jan 8 at 0:10 history edited Ben CC BY-SA 4.0
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Jan 8 at 0:08 answer added Ben timeline score: 4
Jan 7 at 22:54 comment added Henry The probability of a particular child getting $k$ ice creams is simpler: that distribution has a binomial distribution with parameters $10$ and $\frac1{20}$. But what happens to a particular child is not independent of what happens to the others.
Jan 7 at 22:49 comment added Henry I might call it the coupon-collector distribution. There are previous related questions here but briefly, the probability of $x$ children getting at least one ice cream is $S_2(10,x) \, 20! / ((20-x)!\, 20^{10})$ where $S_2(,)$ is a Stirling number of the second kind, the expected number is $20(1-(1-1/20)^{10})$ and the variance is $20(1-1/20)^{10} + 20^2(1-1/20)*(1-2/20)^{10} - 20^2 (1-1/20)^{2\times10}$
S Jan 7 at 21:57 review First questions
Jan 8 at 5:18
S Jan 7 at 21:57 history asked Benjamin Kay CC BY-SA 4.0