Insurance with deductible

[Chandrima]

The question is very simple, but the answer I am getting is £128 . The given answer is £250. Can anyone help me understanding how is it coming to 250??? Also, the explanation the have provided with is quite confusing. Will not the insurer's average claim payout decrease when their is a deductible arrangement? What they have explained is quite opposite. Can anyone help me understanding the concept?

What I used is : below deductible, insurer pays nothing; above deductible, insurer pays claim amt. less deductible.

I am posting the question, given answer and my workout in this thread. Please help.

 

[Varsha Agarwal]

Expected Claim size paid by insurance companies=E(Y)/P(X>100),where y=0,X<100 and y=f(x),x>100.
You didn't divide E(y) with P(x>100).
128/.512=250.

 

[Chandrima]

Expected Claim size paid by insurance companies=E(Y)/P(X>100),where y=0,X<100 and y=f(x),x>100.
You didn't divide E(y) with P(x>100).
128/.512=250.

Thank you Varsha. Yes I got it after posting here.