A Note on the Probability of Winning a Lottery when the Number of Competitors is a Binomial Random Variable (2010)
Type of ContentDiscussion / Working Papers
PublisherCollege of Business and Economics
University of Canterbury. Department of Economics and Finance
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 pi 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.
CitationHogan, S., Meriluoto, L. (2010) A Note on the Probability of Winning a Lottery when the Number of Competitors is a Binomial Random Variable. Department of Economics and Finance. 4pp..
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Keywordsbinomial distribution; binomial theorem; lottery
ANZSRC Fields of Research35 - Commerce, management, tourism and services::3502 - Banking, finance and investment::350208 - Investment and risk management
49 - Mathematical sciences::4905 - Statistics::490506 - Probability theory
38 - Economics::3802 - Econometrics::380202 - Econometric and statistical methods
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