Exercise 2.2 - Legal reasoning

Given the assertation that the criminal has the special blood type, the space of all possibilities contains $800,000\times \frac{1}{100}=8,000$ samples. A sample ${\omega }_i\in \mathrm{\Omega }$ denotes that the $i$-th person with this blood type committed the crime. Let the suspect be the $j$-th person with this special blood type, the event that he/she was the criminal is

For question (a): The probability that an innocent person has this blood type is almost 1%, whose opposite event is the probability that an innocent person has another blood type, which is 99%. This event is different from the suspect is the crimimal.

For question (b): Justice is not measured by probability. More evidence from forensics might increase this probability to unity or reduce it to zero.