Suppose you play die-rolling game in which a fair 6-sided die is rolled once, if

Question

Suppose you play die-rolling game in which a fair 6-sided die is rolled once, if the outcome of the roll (the number of dots on the side facing upward) is divisible by 3, you win as many dollars as the number you have rolled. Otherwise, you loose as many dollars as the number you have rolled. Let X be the profit of the game or the amount of money won or lost per roll. Negative profit corresponds to lost money. What is your profit if the outcome of the roll is 5? Fill out the following probability distribution table Compute the mean or the expected value of x Explain the meaning of the expected value of x in the context of this problem. If you played this game 100 times, how much would you expect to win or loose?

Explanation / Answer

Answer:

a). Profit: -$5   ( or loss of $5)

b).

Roll outcome

profit

P

1

-1

0.1667

2

-2

0.1667

3

3

0.1667

4

-4

0.1667

5

-5

0.1667

6

6

0.1667

c).

Roll outcome

profit x

P

p*x

1

-1

0.1667

-0.16667

2

-2

0.1667

-0.33333

3

3

0.1667

0.5

4

-4

0.1667

-0.66667

5

-5

0.1667

-0.83333

6

6

0.1667

1

Total

-0.5

Expected value = -0.5

d).

In the long run we expect to loose on average of $0.5.

e).

we expect to loose 100*0.5 =$50

Roll outcome

profit

P

1

-1

0.1667

2

-2

0.1667

3

3

0.1667

4

-4

0.1667

5

-5

0.1667

6

6

0.1667

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