Find-the-expected-payback-for-a-game-in-which-you-bet-8-00-on-any-number-from-0-to-99-and-if-your-number-comes-up-you-win-2-000-00-

Question Number 174611 by MathsFan last updated on 05/Aug/22

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{expected}\:\mathrm{payback}\:\mathrm{for}\:\mathrm{a}\: \\ $$$$\mathrm{game}\:\mathrm{in}\:\mathrm{which}\:\mathrm{you}\:\mathrm{bet}\:\$\mathrm{8}.\mathrm{00}\:\mathrm{on}\:\mathrm{any} \\ $$$$\mathrm{number}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{99}\:\mathrm{and}\:\mathrm{if}\:\mathrm{your} \\ $$$$\mathrm{number}\:\mathrm{comes}\:\mathrm{up},\:\mathrm{you}\:\mathrm{win}\:\$\mathrm{2},\mathrm{000}.\mathrm{00} \\ $$

Commented by shikaridwan last updated on 06/Aug/22

$${Probability}\:{of}\:{getting}\:{x}\:\left({x}\in\left[\mathrm{0},\mathrm{99}\right]\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{99}} \\ $$$${not}\:{getting}\:=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{99}}=\frac{\mathrm{98}}{\mathrm{99}} \\ $$$${Expected}\:{payback} \\ $$$$=\$\left(\frac{\mathrm{2000}}{\mathrm{99}}+\frac{\mathrm{98}}{\mathrm{99}}.\mathrm{8}\right)\:\:=\$\mathrm{28}.\mathrm{12} \\ $$

Commented by MathsFan last updated on 09/Aug/22

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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