We know that 8 people have to go to the hospital during a particular week; we need to find the probability that on at least one of the days, at least two people will go to the hospital.

Since there are 8 people who need to go to the hospital and the number of days in a week is 7 , it is not possible that every person visits the hospital on a different day so there must be at least one of the days when at least two people will go to the hospital.

Thus, the probability that on at least one of the days, at least two people will go to the hospital being a sure event is $\(100 \%\)$ i.e. 1 , so the answer is (E).