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Merrill is playing a simple game of dice. For every 6 rolled, Merrill will win $5. For any other number, he must pay $2. How much money can Merrill expect to win or lose?

Respuesta :

Solution -

The probability of getting 6 from a single roll of a fair dice = [tex]\frac{1}{6}[/tex]

The probability of getting any other number rather than 6 would be [tex]1-\frac{1}{6} = \frac{5}{6}[/tex]

So when the outcome is 6, then he wins $5 ,otherwise he has to pay $2

So

E(X) = Expectation value = [tex](\frac{1}{6} )(5) - (\frac{5}{6} )(2)[/tex]                                    ( ∵ $5 gain so +ve and $2 loss so -ve)

=[tex]\frac{-5}{6}[/tex]

∴ So Merrill will lose [tex]\frac{5}{6}[/tex] dollar


Answer: Lose $0.83 APEX

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