Answer:
The least prize size G that I will be willing to buy the lottery is 192
Explanation:
First, Calculate the expected utility
Expected utility = [tex]\sqrt{100}[/tex] = 10
There are two cases
Case 1
I win = 100 - 36 + G = 64 + G
Case 2
I lose = 100 - 36 = 64
Hence the expected utility can be calculated as follow
Expected utility = Chance to win x [tex]\sqrt{( 64 + G )}[/tex] + Chance to lose x [tex]\sqrt{64}[/tex]
10 = 25% x [tex]\sqrt{( 64 + G )}[/tex] + ( 100% - 25% ) x [tex]\sqrt{64}[/tex]
10 = 25% x [tex]\sqrt{( 64 + G )}[/tex] + 75% x 8
10 = 25% x [tex]\sqrt{( 64 + G )}[/tex] + 6
10 - 6 = 25% x [tex]\sqrt{( 64 + G )}[/tex]
4 = 25% x [tex]\sqrt{( 64 + G )}[/tex]
4 / 25% = [tex]\sqrt{( 64 + G )}[/tex]
16 = [tex]\sqrt{( 64 + G )}[/tex]
[tex]16^{2}[/tex] = [tex](\sqrt{( 64 + G )})^{2}[/tex]
256 = 64 + G
G = 256 - 64
G = 192
