dbinom(2,size=5,prob=0.2)[1] 0.2048Participation: Binomial and Poisson in a Biomedical Setting
Solution
Clinical Trial Example
Suppose 5 people receive a new vaccine. From clinical trial data, the probability that any individual experiences a mild side effect (e.g., sore arm, mild fever) is 0.2.
Let \(X\) be the number of people (out of 5) who experience a mild side effect.
Then \(X \sim \text{Binomial}(n=5, p=0.2)\).
Exercise 1
What is the probability that exactly 2 out of 5 people experience a mild side effect? Use the dbinom function.
Exercise 2
What is the probability that at least 1 out of 5 people experiences a mild side effect? (Hint: Use the complement rule: \(P(X \geq 1)=1−P(X=0)\)