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

Solution -

The probability of getting 6 from a single roll of a fair dice = $\frac{1}{6}$

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

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

So

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

=$\frac{-5}{6}$

∴ So Merrill will lose $\frac{5}{6}$ dollar

Answer 2

Answer: Lose $0.83 APEX