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 $500 bet), for a net gain of $99 comma 500. what is the probability of winning?

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

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

[tex]100,000p-500=100\implies p=\dfrac3{500}=0.006[/tex]

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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 ​$500 ​bet), for a net gain of ​$99 comma 500. what is the probability of​ winning?

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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 $500 bet), for a net gain of $99 comma 500. what is the probability of winning?