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Roulette (Posted on 2005-03-23) Difficulty: 2 of 5
If I spin the roulette (numbers from 0 to 36) N consecutive times, how many different numbers should I expect to get?

(If N=1, your formula should give 1 as an answer, but for N=2, it should be a little under 2, and for all other N, the formula should be less than the minimum of N and 37.)

Another question: how many times should you spin the roulette, so chances are better than one in a million, that all 37 numbers will have appeared?

See The Solution Submitted by e.g.    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips Hadn't noticed this while it was in the queue, but ... (part 1 spoiler) | Comment 1 of 4

Part 1 is the same situation as in Playing Lotto, and the solution is similar: plagiarizing my own post on that,

Each of the 37 numbers has 36/37 probability of not being hit on a particular roll, and (36/37)^N of not being hit on any of the n spins.

While the choices are not independent, that is, if one number is known not to have occurred, the others are all the more likely to have occurred, the expected value of the total of all these 1's (present) and 0's (absent) is still the sum of the expected values of each event (i.e., the event that the first number, second number, etc. is present).

So the expected number of non-hit numbers is 37*(36/37)^N, and the expected number of different numbers hit is then 37*(1-(36/37)^N) 

 


  Posted by Charlie on 2005-03-23 15:05:14
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