Revision as of 15:27, 26 June 2024 by Admin (Created page with "'''Solution: C''' If <math>n_0</math> people are tested then the number of people with a particular rare blood type has a binomial distribution with <math>n=n_0, p=0.001 </math>. We need to find the smallest <math>n_0</math> such that <math display = "block"> P(N \geq 1) = 1 - (1-p)^{n_0} \geq 1/2 \implies n_0 \geq \frac{\log(1/2)}{\log(1-p)} = 692.81 </math> Hence the answer is <math>n_0 = 693 </math>.")
Exercise
ABy Admin
Jun 26'24
Answer
Solution: C
If [math]n_0[/math] people are tested then the number of people with a particular rare blood type has a binomial distribution with [math]n=n_0, p=0.001 [/math]. We need to find the smallest [math]n_0[/math] such that
[[math]]
P(N \geq 1) = 1 - (1-p)^{n_0} \geq 1/2 \implies n_0 \geq \frac{\log(1/2)}{\log(1-p)} = 692.81
[[/math]]
Hence the answer is [math]n_0 = 693 [/math].