Answer:
0.9091 = 90.91% probability that a person flagged as a future criminal by the Precogs will actually commit a crime
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Flagged as future criminal
Event B: Commits a crime.
In the year 2054 the government estimates that out of every 1,000,100 citizens 1,000,000 will remain law-abiding, and 100 will eventually commit a crime.
This means that
If a person is going to commit a crime, the Precogs identify that person correctly 99.999% of the time
This means that
Probability of being identified as a criminal:
0.99999 out of 0.00009999(identified and commits crime).
(1-0.99999) out of (1-0.00009999) (identifed and does not commits crime). So
What is the probability that a person flagged as a future criminal by the Precogs will actually commit a crime
0.9091 = 90.91% probability that a person flagged as a future criminal by the Precogs will actually commit a crime