Question

Ray and Jon play a game of chance with two dice. If the sum of the dice is seven, Ray pays Jon $15. But if the sum is anything else, Jon pays Ray $10. What is the expected value of the game for Jon?Answer:

Answer 1

Step 1

`\text{Probability of any event = }\frac{\text{number of required outcomes}}{n\text{umber of possible outcomes}}`

Step 2:

Draw the table of the possible outcomes.

Step 3:

Draw the table for the expected value

Number of the sum of seven = 6

Number of anything else = 30

Total possible outcomes = 36

`\begin{gathered} \text{Expected value formula = Value }*\text{ Probability of event} \\ \text{Expected value formula = xp(x)} \end{gathered}`

Final answer

The expected value of the game for Jon

`\begin{gathered} =\text{ }(15)/(6)\text{ + }(50)/(6) \\ =\text{ }(65)/(6)\text{ } \\ =\text{ 10.83} \end{gathered}`