1. The number of times that a person contracts a cold in a year is a Poisson random variable with parameter lambda=5. Suppose a wonder drug reduces the Poisson parameter to lambda=3 for 75% of the population but does not affect the rest of the population. If an individual tries the drug for a year and contracts two colds in that time, how likely is it that the drug is beneficial for him or her 2. Probability mass fn is given by ((lambda^k) * e^(-lambda))/k_factorial 3. The attempt at a solution Here's where I'm confused. The probabiliy mass fn gives the probability that a person contracts k number of colds in a given year, correct? In this problem, I solved the probability mass function with the constraints (lambda=3, k=2) and (lambda=5, k=2). When lambda=3 it means the medicine worked and the person should have a smaller chance of contracting two colds (k=2) in a given year than when lambda=5, when the drug has not worked. However, when I calculate those two values, the probability is 0.224 when lambda=3 and 0.08422 when lambda=5. Sometimes, the textbook has solutions to problems involving Poisson distribution where the answers are in the form 1 - e^(-n) where n is a positive integer. Am I supposed to take the complement of this? Why is the probability of contracting two colds in a year higher when the medicine works? I'm just having so much trouble with random variables, I'd really appreciate it if someone can provide any links to video lectures or helpful guides out there. Thank you!