Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 6 or a 3,nothing otherwise.What is the expected amount you win?
A)$2.00
B)-$0.67
C)$4.00
D)-$2.00
E)$0.00

Question

Quizplus · Accepted Answer

The probability of rolling a 6 or 3 is $\frac{2}{6} = \frac{1}{3}$ since the die is fair. 
The probability of rolling anything else is $1-\frac{1}{3} = \frac{2}{3}$.

Thus, the expected value of the game is: 
$E(	ext{winning}) = (\frac{1}{3})(4.00) + (\frac{2}{3})(-2.00) -  2.00$
$E(	ext{winning}) = \frac{4}{3} - \frac{4}{3} - 2.00$
$E(	ext{winning}) = -\frac{2}{3}$
Therefore, the expected amount to win is -$0.67.

Suppose You Pay $2