I am currently studying the following case of Neil Owen, based on the following article I found a newspaper:
"A 20-year-old student was jailed for life yesterday for the brutal rape and murder of a schoolgirl, after one of the biggest DNA testing programmes in British criminal history. Neil Owen was arrested a year after the murder when his genetic fingerprint was matched with DNA found at the scene, following a mass DNA screening of 2000 men on the estate. He lived just 100 yards from the victim's house. Laboratory tests revealed the chances of anyone else being the killer were 1 in 160 million."
Now first of all I am aware that there is an issue with prosecutors fallacy here. Because the 1 in 160 million is interpreted as P(innocence|matching blood type evidence) when it actually refers to P(matching blood type evidence|innocence). But my question refers to the reasoning of the defence.
Counsel for the defence pointed out that there are about 30 million males in the United Kingdom, and argued that the correct probability that Owen was guilty is about 16/19, not high enough to convict beyond a reasonable doubt. So my two questions are
1. How do you think that the figure 16/19 was calculated? (I am sure the population of 30 million and the probability of 1 in 160 million was used?)
2. What implicit assumptions were made, and how reasonable are they?