You roll a die. if it comes up a 6, you win $100. if not, you get to roll again. if you get a 6 the second time, you win $50. if not, you lose. a. create a probability model for the amount you win.

b. find the expected amount you'll win.

c. what would you be willing to pay to play this game?

a.

x $         0 $         50         $ 100

p (x)    25/36      5/36        6/36

b. 23.61%

c. 23.61%

Step-by-step explanation:

We have that "x" is the amount of money earned:

we have to fail twice, the probability of failure is 5/6 and the probability of hitting is 1/6, therefore if you lose the probability would be:

5/6 * 5/6 = 25/36

the one to win 50 $, would be:

1/6 * 5/6 = 5/36

and the one to win $ 100 would be:

1/6 * = 6/36

that is to say:

a.

x $         0 $         50         $ 100

p (x)    25/36      5/36        6/36

b. the expected amount you'll win would be:

0 * 25/36 + 50 * 5/36 + 100 * 6/36 = 23.61

c. The normal thing is to pay at least the expected amount, that is, $ 23.61, since something greater than that would already be profit.

x = 3 ± √(5+y)