what is the probability exactly 3 people will have side effects if 150 people r tested n 3%

Question

What is the probability that exactly 3 people will have side effects if 150 people are tested and there is a 3%

Answer 1

P=3% probability of side effects. (P+(1-P))^150=1 represents the sum of all individual  probabilities (binomial distribution). For exactly 3 out of 150, we need to compute the fourth term in the expansion. The probability of no people with side effects is (1-P)^150; 1 person: 150P(1-P)^149; 2 people: (1/2)150*149P^2(1-P)^148; 3 people: (1/6)150*149*148P^3(1-P)^147=0.1691 or 16.91%.