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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.

Suggested Citation

  • Seamus Hogan & Laura Meriluoto, 2010. "A Note on the Probability of Winning a Lottery when the Number of Competitors is a Binomial Random Variable," Working Papers in Economics 10/48, University of Canterbury, Department of Economics and Finance.
  • Handle: RePEc:cbt:econwp:10/48
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    File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1048.pdf
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    Keywords

    Binomial Distribution; Binomial Theorem; Lottery;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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