Answer to Question #205144 in Statistics and Probability for Shema Derrick

Question #205144

.The probability that a patient recovers from a delicate heart operation is 0.8. What is the probability that: a) exactly 2 of the next 3 patients who have this operation will survive? b) all of the next 3 patients who have this operation survive?


1
Expert's answer
2021-06-16T14:28:46-0400

Binomial distribution

p=0.8

n=3

P(x)=(nx)Px(1P)nx,x=0,1,2...,n.P(x)=\binom{n}{x}P^x(1-P)^{n-x}, x=0,1,2...,n.

a.P(x=2)a. P(x=2)

P(x=2)=(32)0.820.2=0.384P(x=2)=\binom{3}{2}0.8^20.2=0.384

b. P(x=3)P(x=3)

P(x=3)=(33)0.83=0.512P(x=3)=\binom{3}{3}0.8^3=0.512


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