The desired probability that more than 3 students withdraw was determined to be
f(4) + f(5) + + f(18).
Recall that the sum of the probabilities for an experiment must be 1. Thus, it must be the case that the sum of the probabilities for each event of x students withdrawing from the class will be 1. That is,
f(0) + f(1) + + f(18) = 1.
Therefore, we have the following.
f(0) + f(1) + f(2) + f(3) + f(4) + + f(18) = 1
Solve this equation for the desired probability,
f(4) + f(5) + + f(18).
f(4) + f(5) + ... + f(18) = 1 + (f(0) + f(1) + f(2) + f(3))f(4) + f(5) + ... + f(18) = 1 − (f(0) + f(1) + f(2)) f(4) + f(5) + ... + f(18) = 1 + (f(0) + f(1) + f(2))f(4) + f(5) + ... + f(18) = 1 − (f(0) + f(1) + f(2) + f(3))