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A Note on the Probability of Winning a Lottery when the Number of Competitors is a Binomial Random Variable

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Abstract

Consider a model in which a consumer faces a lottery with j other people for a prize, so that the probability of winning the prize is 1/(j+1). Now let j be a random variable, determined by the binomial distribution. Specifically, let there be n potential competitors for the consumer in the lottery, each with an independent probability of ? of being a competitor. In this note, we show how the resulting expression for the expected value of 1/(j+1) using binomial probabilities can be simplified by means of the binomial theorem.

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File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1048.pdf
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Bibliographic Info

Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/48.

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Length: 4 pages
Date of creation: 11 Aug 2010
Date of revision:
Handle: RePEc:cbt:econwp:10/48

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Keywords: Binomial Distribution; Binomial Theorem; Lottery;

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