In the Fall of 2012, a huge man-hunt took place for the sniper who killed a numb
ID: 3199565 • Letter: I
Question
In the Fall of 2012, a huge man-hunt took place for the sniper who killed a number of people in Washington, D.C., and surrounding areas.
Early in the search, the police arrested a man who owned a white van, a number of rifles, and a manual for snipers. It was thought at the time that there was one sniper and that he owned all these items, so for the sake of this story let’s assume that these facts are true.
Now, suppose that there are around 4 million people in the DC area, and also suppose that only ten of these people own all three items.
(a) What is the probability that an innocent man would own all these items?
(b) What is the probability that a man who owned all these items would be innocent?
(c) Can you give a similar example regarding the probability in a population (statistic meaning, not necessarily a population of people)?
Explanation / Answer
a) There is only one sniper and 10 people possessing all the three items
Number of innocent people possesing three items = 10 - 1(guilty sniper) = 9
Probability that innocent man would own all these items = Number of innocent people possessing three items/Total population = 9/4,000,000
b) There are 10 people who own all three items and 1 person who is guilty
Probability that man who owned all three items would be innocent = 9/10 = 0.9
c) The other famous example will be virus infected people, with total population, number of cases with people infected having some three symptoms. So can find the people who will be treated with virus but are safe