Paying $6 (Getting -$6) means that you managed to roll a 1 or 2.
This probability is given as:
[tex]P=\frac{\text{expected outcome}}{\text{sample space}}[/tex]
Therefore, probability of rolling a 1 or 2:
[tex]P(1or2)=\frac{2}{6}=\frac{1}{3}=0.333[/tex]
Getting $4 means that you managed to roll a 3, 4 or 5. This probability is:
[tex]P(3\text{ or 4 or 5)=}\frac{\text{3}}{6}=\frac{1}{2}=0.5[/tex]
Our new table is therefore:
b. The expected Profit = -6(0.3333) + 4(0.5) + 9(0.1667) = $1.50
c. If you play many games, you will likely win on average, close to $1.50
d. Since the expected value is positive, you are likely to come back with a positive value if you played many games.
