Consider a lottery in which 100 tickets are sold for eachdrawing, and each ticke

Question

Consider a lottery in which 100 tickets are sold for eachdrawing, and each ticket costs $1. Exactly one ticket wins in eachdrawing. Suppose you have $50 to invest in the lottery. Youconsider two possible strategies: Strategy One: Spend $50 in one drawing, e.g. buy 50 ticketsfor a single drawing. Strategy Two: Spend $1 in 50 drawing, e.g. buy 1 ticket foreach of 50 different drawings. (a) Determine the probability of winnig the lottery at leastonce under each strategy. (b) Suppose your goal is to maximize your probability ofwinning the lottery at least once. Which strategy would youchoose? Consider a lottery in which 100 tickets are sold for eachdrawing, and each ticket costs $1. Exactly one ticket wins in eachdrawing. Suppose you have $50 to invest in the lottery. Youconsider two possible strategies: Strategy One: Spend $50 in one drawing, e.g. buy 50 ticketsfor a single drawing. Strategy Two: Spend $1 in 50 drawing, e.g. buy 1 ticket foreach of 50 different drawings. (a) Determine the probability of winnig the lottery at leastonce under each strategy. (b) Suppose your goal is to maximize your probability ofwinning the lottery at least once. Which strategy would youchoose?

Explanation / Answer

So let's determine the probability. 1. Since we bought 50 tickets out of 100, we would have50/100 = 1/2 chance of winning. 2. Binomial probability = Success of 1 or more ticketswinning. Let's subtract the probability of 0 from that. .99^50 =.605 1- .605 = .395 probability of winning if we bought 1 ticketfor each of 50 different drawings. If we want to maximize the probability of winning the lotteryat least once, we would choose option 1. (.5 >.395).

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