Answer to Question #224878 in Statistics and Probability for Shaban

Question

An allergist claims that 45% of the patients she tests are allergic to some type of weed. What is the probability that (i) exactly 4 of her next 5 patients are allergic to weeds? (ii) none of her next 5 patients is allergic to weeds?

Answer 1

Let $X=$ the number of patients who is allergic to weeds: $X\sim Bin(n, p).$

Given $n=5,p=0.45, q=1-p=0.55.$

(i)

$$P(X=4)=\dbinom{5}{4}(0.45)^4(0.55)^{5-4}$$

$$=0.1127671875$$

(ii)

$$P(X=0)=\dbinom{5}{0}(0.45)^0(0.55)^{5-0}$$

$$=0.0503284375$$