Answer:
Step-by-step explanation:
Given that if an odd number comes up, you lose.
i.e. [tex]P(losing) = P(1,3,5) = \frac{1}{2}[/tex]
[tex]P(win 60) = P(6) =\frac{1}{6} \\[/tex]
If you get 2 or 4 you roll again
Thus rolling again prob = [tex]\frac{2}{6} =\frac{1}{3}[/tex]
After rolling II time, if get 6, win otherwise lose.
Thus winning amounts A canbe
0 36 60
[tex]P(0) = \frac{1}{2}+\frac{1}{3} (\frac{5}{6})=\frac{7}{9} \\P(36) = \frac{1}{3} (\frac{1}{6})=\frac{1}{18}\\P(60) =\frac{1}{6}[/tex]
This is a genuine pdf since prob >0 and total prob = 1.
b)Expected gain = sum of gain * prob = [tex]\frac{7}{9} (0)+\frac{1}{18} (36)+\frac{1}{6} (60)\\=12[/tex]
Thus I would be willing to pay an amount atmost 12 dollars.
