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