Question

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?

Answer 1

Answer: Lose $0.83 APEX

Answer 2

The probability of getting 6 from a single roll of a fair dice =
`(1)/(6)`

The probability of getting any other number rather than 6 would be
`1-(1)/(6) = (5)/(6)`

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

So

E(X) = Expectation value =
`((1)/(6) )(5) - ((5)/(6) )(2)` ( ∵ $5 gain so +ve and $2 loss so -ve)

=
`(-5)/(6)`

∴ So Merrill will lose
`(5)/(6)` dollar