Calculating Probabilities in Criminal Verdicts: Innocence and Guilt Explained

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In summary, when a court returns three verdicts of 'guilty', 'not guilty', and 'not proven', with 65% of the verdicts being 'guilty', 25% being 'not guilty', and 10% being 'not proven', the probability of an accused person being innocent is 28.75%. To find the probability of an innocent person being found guilty, Bayes theorem must be applied to determine the likelihood of the person being guilty given the verdict of 'guilty'.
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Homework Statement


A 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!
 
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  • #2
You need to find what P(E_1|g) is. However, you only know what P(g|E_1) is. In this situation, the only thing which you can do is applying Bayes theorem...
 

Related to Calculating Probabilities in Criminal Verdicts: Innocence and Guilt Explained

1. How do you calculate the probability of innocence or guilt in a criminal verdict?

Calculating the probability of innocence or guilt in a criminal verdict involves analyzing all the evidence presented in a case, considering the credibility of witnesses, and evaluating the strength of the prosecution's case. This can also include statistical analysis of previous similar cases and the use of expert witnesses to provide their opinions.

2. What factors are considered when determining the probability of innocence or guilt?

Factors that are considered when determining the probability of innocence or guilt include the credibility of witnesses, physical evidence, witness testimonies, alibi, motive, and the defendant's previous criminal record. Other factors such as the prosecution's burden of proof, the defense's arguments, and the judge's instructions to the jury may also be taken into account.

3. Can the probability of innocence or guilt be accurately determined?

No, the probability of innocence or guilt cannot be accurately determined. It is ultimately up to the jury to weigh all the evidence presented and make a decision based on the reasonable doubt standard. However, statistical analysis and expert opinions can help guide the jury in their decision-making process.

4. How does DNA evidence affect the calculation of probabilities in criminal verdicts?

DNA evidence can play a significant role in calculating probabilities in criminal verdicts. It can provide strong scientific evidence that can prove or disprove a defendant's involvement in a crime. The use of DNA evidence has led to many exonerations and has also helped convict the guilty, making it a crucial factor in determining the probability of innocence or guilt.

5. How can the probability of innocence or guilt impact the outcome of a criminal trial?

The probability of innocence or guilt can greatly impact the outcome of a criminal trial. If the probability of guilt is high, the jury is more likely to convict the defendant. On the other hand, if the probability of innocence is high, the jury may be less likely to convict. Ultimately, the jury's decision will be based on the evidence presented and the reasonable doubt standard, but the probability of innocence or guilt can influence their decision-making process.

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