DSE 2013 ques 6 Help

[cheesecake]

I did it this way -
Utility without lottery = 10 (100)^1/2 = 100
Expected value of lottery = 400p+49(1-p) = 351p+49
Utility of expected value of lottery =10(351p+49)^1/2
Equating this to 100 for indifference, we get p = 51/351
But the answer is p>51/221 and not 51/351 !

I also tried another way
I found Utility of the lottery = p U(winning)+(1-p) U(losing) = p 10(400)^1/2 + (1-p) 10(49)^1/2 = 130p+70
Equating to 100 for indifference, p = 3/13
This p is equal to the answer given

How is this happening??

[Anand]

NetPayoff      Probability
-51                 (1-p)
300                   p

probability must be >0

300p-51+51p>0

p>51/351

I saw this in a book.

[cheesecake]

Anand I thought so too but the answer is p>51/221 and the second way yields the correct answer. That is why i am getting so confused

[Anand]

New answer:

The person is risk averse.She will play the  lottery if expected utility from lottery must be greater than utility of wealth.

EU =10(P)(400)^1/2+10(1-P)(49)^1/2>100

P>3/13

Multiplying it by 17 , we get
51/221.