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

Seamus Hogan and Laura Meriluoto

Working Papers in Economics from University of Canterbury, Department of Economics and Finance

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.

Keywords: Binomial Distribution; Binomial Theorem; Lottery (search for similar items in EconPapers)
JEL-codes: C10 C16 (search for similar items in EconPapers)
Pages: 4 pages
Date: 2010-08-11
New Economics Papers: this item is included in nep-upt
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