Answer to Question #264203 in Statistics and Probability for Honour

Question #264203

in clinical trials a certain drugs has a 8% success rate of curing a known diseases. If 15 people are known to have the diseases, what is the probability that at least 2 are cured?


1
Expert's answer
2021-11-11T18:54:57-0500

Let "X=" the number of cured people: "X\\sim Bin(n, p)."

Given "n=15, p=0.08, q=1-p=1-0.08=0.92."

Then


"P(X\\geq2)=1-P(X=0)-P(X=1)"

"=1-\\dbinom{15}{0}(0.08)^0(0.92)^{15-0}-\\dbinom{15}{1}(0.08)^1(0.92)^{15-1}"

"\\approx1-0.28629740407-0.37343139661"

"\\approx0.340271"


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