I have only one doubt here:
One way :
We know probability for every person getting right hat is 1/100 hence
Expectation = 1*(1/100) + 1*(1/100) + 1*(1/100) + ... 100 times = 1
Its the answer.
Another way :
If there are 100 person from 1,2...100
then it should be : 1*(1/100) + 2*(1/100) + 3*(1/100) + ........ = 50.5
How to know which one to use
Answer is 1 though