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.]