2.5 Are You Sherlock? (10 pts) A murder was committed in Gotham city last night.
ID: 3699164 • Letter: 2
Question
2.5 Are You Sherlock? (10 pts) A murder was committed in Gotham city last night. The police found the perpetrator's DNA on the crime scene and ran it against a database of 20,000 people. A match was found and it turns out to be your best friend. He/She is arrested and is due in court tomorrow. Given your prowess in CS206, your friend has hired you as his/her lawyer. The prosecution's argument is the following: "It is a well known statistical fact that the chance that two people's DNA matches is 1 in 10,000. Hence the chance that the defendant is innocent is 1 in 10,000. Hence with overwhelming probability the person is guilty". Use probability to come with a rigorous counter argument that can save your friend. [Note: You can take it that the statistical fact stated by the prosecution is indeed correct.]Explanation / Answer
It is given that it is a well know statistical fact that the chance of two people's DNA being same is 1 in 10000. But this fact does not prove my friend guilty. Statistical facts are derieved after doing research on large amount of dataset.
Chances of two peoples' DNA being same is 1 in 10000 means if we perfor DNA test on large number of people say 1000000000, on an average there will be only one person in 100000 persons who DNA is similar to any one of the 10000.
Now let analyse the situation carefully, on an average, there is 1 such person, then among 100000000 peoples, there will be on an average 10000 peoples whose DNA matches with some other persons. If we pick a number of people, there are chances that these people are picked up and the person with whom their DNA matches is not picked up. DNA matching is thus not a concrete proof.
It is no surprize if my friends DNA matches with some person. It doesn't make him guilty. If he is proved to be guilty now, there is no justice for those 10000 persons among 100000000 persons whose DNA matches with some perpetrator.
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