Answer to Question #224878 in Statistics and Probability for Shaban

Question #224878

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?


1
Expert's answer
2021-08-10T14:59:15-0400

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

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

(i)


P(X=4)=(54)(0.45)4(0.55)54P(X=4)=\dbinom{5}{4}(0.45)^4(0.55)^{5-4}

=0.1127671875=0.1127671875

(ii)


P(X=0)=(50)(0.45)0(0.55)50P(X=0)=\dbinom{5}{0}(0.45)^0(0.55)^{5-0}




=0.0503284375=0.0503284375

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