Solution -
The probability of getting 6 from a single roll of a fair dice =
The probability of getting any other number rather than 6 would be
So when the outcome is 6, then he wins $5 ,otherwise he has to pay $2
So
E(X) = Expectation value = ( ∵ $5 gain so +ve and $2 loss so -ve)
=
∴ So Merrill will lose dollar