Hi!

Here's the question I need help with:

Consider a hypothetical town with population 10,000 in which a man is suspected of a crime. His blood matches a stain found at the scene some time after the crime was committed. 1% of the population will have matching blood. Because in this case the stain is somewhat degraded, the probability of getting a match even if the blood is identical is 0.95

a) Draw a tree of the different possibilities of the man being guilty or not, and his blood matching or not.
b) Find the probability of a match.
c) Find the probability that this man is guilty of the crime and his blood matches.
d) If there is a match, find the probability that the man is guilty (use Bayes' rule)

Thanks in advance.

There are four possibilities to consider. They are:

He is guilty and his blood matches.
He is guilty and his blood doesn't match.
He is not guilty and his blood matches.
He is not guilty and his blood doesn't match.

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What are the percentages for each possibility? This is where I'm getting confused.

Do you understand conditional probability?

Pr(not guilty | blood matches) = 0.01.

etc.

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1. There are two things you should never try to prove ...... the impossible and the obvious.

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4. Pressure makes diamonds.