Abstract
Consider the well-known card collector’s problem in which each card has a different probability of being drawn. Using the principle of inclusion–exclusion we derive the probability of obtaining a complete collection and compute the expected value of the number of cards that need to be bought to complete the collection. In particular we obtain an interesting identity when the cards have equal probabilities.
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Acknowledgements
Presentation of the results at the UNCG Regional Mathematics and Statistics Conference was made possible by a Mentor Protégé grant offered by the College of Sciences and Mathematics at Kennesaw State University.
We would like to thank the referee for carefully reading the paper and making some useful suggestions.
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Gadidov, A., Thomas, M. (2013). The Card Collector Problem. In: Rychtář, J., Gupta, S., Shivaji, R., Chhetri, M. (eds) Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference. Springer Proceedings in Mathematics & Statistics, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9332-7_12
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DOI: https://doi.org/10.1007/978-1-4614-9332-7_12
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