Tom J.

asked • 06/14/17

Cereal company is giving away six different prizes. Each box contains one prize. How many cereal boxes should I buy to get all of the prizes that are offered?

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Kenneth S. answered • 06/14/17

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This is not a wise endeavor; there will be thousands of boxes, and your chances of getting ANY one of 6 prizes (if that's really the limited total) are very small. You'd waste a lot of money trying to get all of the prizes, and also there would be the problem of storing numerous cereal boxes. you might not even be able to afford the milk to pour into each bowl of the cereal, which you'd be obligated to use, not waste, over a LONG time. You'd get sick of cereal.
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Paul M.

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This is not an elementary problem and I cannot give you a precise answer, but I can tell you that if you bought 19 boxes you would have about a 20% chance of getting all 6 prizes.  I did not push the calculation on my spreadsheet any further, but it could be done; the numbers get pretty big.  I also cannot tell you the expected number of boxes to get the 6 prizes because I am not sure of the distribution function needed (i.e. it is at the moment beyond my expertise!).
 
In order to understand the complexity of the problem you should refer to:
"An Introduction to Probability Theory and Its Applications", Volume I, 2nd Edition by William Feller.
This classic book was published in 1957 and is still a standard reference.
 
I want to thank you for asking this question because it has required me to do a lot of thinking and reading and understanding.  Good luck!
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04/19/18

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