Answer to Question #315406 in Statistics and Probability for Nimi

Question

Tubeit-Biner et al. (A-9) found that the number of serious gastrointestinal reactions reported to British Committee on Safety of Medicine was 538 for 9,160,000 prescriptions of the anti-inflamma drag piroticam. This corresponds to a rate of 058 gastrointestinal reactions per 1000 prescriptio written. Using a Poisson model for probability, with A-06, find the probability of (a) Exactly one gastrointestinal reaction in 1000 prescriptions (b) Exactly two gastrointestinal reactions in 1000 prescriptions (c) No gastrointestinal reactions in 1000 prescriptions (d) At least one gastrointestinal reaction in 1000 prescriptions

Answer 1

$\lambda=0.06$

x=1

$P(X=x)=\frac{\lambda^xe^{-\lambda}}{x!}$

a. $P(1)=\frac{0.06^1e^{-0.06}}{1}=0.057$

b. $P(2)=\frac{0.06^2e^{{-0.06}}}{2}=0.0017$

$c. P(0)=\frac{0.06^0e^{{-0.06}}}{1}=0.942$

d. P=1-P(0)=1-0.942=0.058