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

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

I used Poisson distribution in order to find probability.

\[\lambda \ = \frac{1}{1000}\] Time interval is 10000

\[p(0,10000/1000) = p(0,10) = \frac{\lambda\ ^0*e^{-10}}{0!} = e^{-10}\]

exp(1)^(-10)
## [1] 4.539993e-05
  1. 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?

\[p = \frac{1}{2}\]

\[\lambda \ = \frac{n}{1000}\]

Finding n:

\[\frac{1}{2} = \frac{(\frac{n}{1000})^0*e^{-n/1000}}{0!} = e^{-n/1000}\] \[ e^{-n/1000} = \frac{1}{2}\] \[n = 1000*ln2\]

round(1000*log(2),0)
## [1] 693