An easier way to do it is to use the normal distribution, or central limit theorem. My post on the theorem illustrates that a sample will follow normal distribution if the sample size is large enough. We will use that as well as the rules around determining probabilities in a normal distribution, to arrive at the probability in this case.
Problem: I have a group of 100 friends who are smokers. The probability of a random smoker having lung disease is 0.3. What are chances that a maximum of 35 people wind up with lung disease?
Click through for the example.