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

Question

.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?

Answer 1

Binomial distribution

p=0.8

n=3

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

$a. P(x=2)$

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

b. $P(x=3)$

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