A crime-scene DNA sample is compared against a database of 50000 people. A match is found, and that person is then accused of the crime. At the trial, it testified that the probability that two DNA profiles match by chance is only 1 in 40000. Because the probability of an innocent person matching the crime scene DNA is so tiny, the person is convicted of the crime. ( In the language of hypothesis testing, it would be to test ?0:H0: man is innocent vs. ??:HA: man is not innocent and reject ?0H0 based on the p-value of 140000140000 = 2.5x10-5 However, the argument used was fallacious. People may often confuse this p-value with the probability the suspect is innocent, but this is not the case . Since 50000 people were tested, there were 50000 opportunities to find a match by chance. Even if none of the people in the database left the crime-scene DNA, you will show below that a match by chance to an innocent person is more likely than not. Therefore, the evidence, taken alone, is an uncompelling data dredging result. If the culprit were in the database. then the culprit and one or more other people would probably be matched. Regardless, it would be a fallacy to ignore the number of records searched when weighing the evidence. Assuming the 50000 people comprise an (independent) random sample, what is the probability there will be at least one matching the DNA at the crime scene? Answer Answer as a decimal between 0 and 1 accurate to 4 or more decimal places. (Hint: this is similar to some problems done in section 2.5. )
A crime-scene DNA sample is compared against a database of 50000 people. A match is found, and that person is then accused of the crime. At the trial, it testified that the probability that two DNA profiles match by chance is only 1 in 40000. Because the probability of an innocent person matching the crime scene DNA is so tiny, the person is convicted of the crime.
( In the language of hypothesis testing, it would be to test
?0:H0: man is innocent vs. ??:HA: man is not innocent
and reject ?0H0 based on the p-value of 140000140000 = 2.5x10-5
However, the argument used was fallacious. People may often confuse this p-value with the probability the suspect is innocent, but this is not the case . Since 50000 people were tested, there were 50000 opportunities to find a match by chance.
Even if none of the people in the database left the crime-scene DNA, you will show below that a match by chance to an innocent person is more likely than not. Therefore, the evidence, taken alone, is an uncompelling data dredging result. If the culprit were in the database. then the culprit and one or more other people would probably be matched. Regardless, it would be a fallacy to ignore the number of records searched when weighing the evidence.
Assuming the 50000 people comprise an (independent) random sample, what is the probability there will be at least one matching the DNA at the crime scene? Answer
Answer as a decimal between 0 and 1 accurate to 4 or more decimal places.
(Hint: this is similar to some problems done in section 2.5. )
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