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tigry1 [53]
3 years ago
6

A game has an expected value to you of ​$100. it costs ​$500 to​ play, but if you win you receive​ $100,000 (including your ​$50

0 ​bet), for a net gain of ​$99 comma 500. what is the probability of​ winning?
Mathematics
1 answer:
tekilochka [14]3 years ago
8 0

Let X be a random variable denoting the amount of winnings in any given round of the game. There is some probability p of winning where P(X=99,500)=p, while P(X=-500)=1-p, assuming these are the only two possible outcomes. So we have

\mathbb E[X]=\displaystyle\sum_xxP(X=x)=99,500p-500(1-p)=100

100,000p-500=100\implies p=\dfrac3{500}=0.006

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