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Homework Statement
A court returns three verdicts. ‘guilty’, ‘not guilty’ and
‘not proven’. 65% of the verdicts were ‘guilty’, 25% of the verdicts
were ‘not guilty’ and 10% were ‘not proven’.
When the court’s verdict is ‘guilty’ 5% of the accused/tried are actually innocent. The corresponding probabilities for the verdicts ‘not guilty’ and ‘not proven’ are 0.90 and 0.30, respectively.
(a) What is the probability that an accused person is actually innocent?
(b) What is the probability that an innocent person will be found guilty?
Homework Equations
The Attempt at a Solution
I know how to do Question 1.
accused = 100%
f= innocent
E1=guilty
E2=not guilty
E3=not proven...therfore maximum of 3 events possible
E1, E2, E3=Accused = 100%
Using law of total probability p(f)=p(f|E1)P(E1) + p(f|E2)P(E2)...n times
p(f)=p(f|E1)P(E1) + p(f|E2)P(E2)+ p(f|E2)P(E3)
p(f|E1)=0.05
p(f|E1)=0.9
p(f|E1)=0.3
...all other info is given also
= 0.05 × 0.65 + 0.90 × 0.25 + 0.30 × 0.10
= 0.2875
HOW DO YOU DO Question 2!