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On the average, only 1 person in 1000 has a particular rare blood type.

a) Find the probability that, in a city of 10,000 people, no one has this blood type.

b) How many people would have to be tested to give a probability greater than 1/2 of finding at least one person with this blood type?

 Feb 17, 2020
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\(p=0.001\\ a)~P[\text{no one in 10000 has blood type}]=\left(1-0.001\right)^{10000} = \\ (0.999)^{10000} = 0.0000451733\\~\\ b)~P[\text{at least 1 w/type in $n$ tested}] = \\ 1-P[\text{none w/type in $n$ tested}]=\\ 1-(1-0.001)^n = 1-(0.999)^n \geq \dfrac 1 2\\ \dfrac 1 2 \geq (0.999)^n\\ \ln(1/2)\geq n \ln(0.999)\\ \dfrac{\ln(0.5)}{\ln(0.999)} \leq n\\ n \geq 693\)

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 Feb 18, 2020

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