1. ## Probability tree diagram

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 diagram of the different possibilities of the man being guilty or not and his blood matching or not.

I know how to do a tree diagram except the wording of this problem is a bit confusing. For the first branch would it be 0.95 for blood match, 0.05 blood not match and then what? :s please help.

2. Originally Posted by princess_anna57
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 diagram of the different possibilities of the man being guilty or not and his blood matching or not.

I know how to do a tree diagram except the wording of this problem is a bit confusing. For the first branch would it be 0.95 for blood match, 0.05 blood not match and then what? :s please help.
Your first branch would be the blood matching and then it will be the 0.95 blood match

3. So I got 0.01 blood match and 0.99 blood not match in the population and then for the second branch of blood match, i got 0.95 blood match and 0.05 blood not match for this case. For the 0.99 blood not match, it's just zero for the second branches huh?

Nooo... it's wrong, the question is asking...of the different possibilities of the man being guilty or not and his blood matching or not

if he's guilty, it's 1/10,000 (because only one person can be guilty).... gah so confused and blood match is 0.95

4. Originally Posted by princess_anna57
So it would be the 1% out of 10,000 which is 100/10000 and then the 0.95% bit? Cool.
1% of 10,000 is 10,000/100 = 100. Then you'd do the 0.95 part

5. Nah it still doesn't make sense. I have now...0.95 blood match and 0.05 blood not match and then for the second branch of blood match, i have man guilty 0.01 and man not guilty 0.99. do i just write zero for the second branch of blood not match?

6. Originally Posted by princess_anna57
Nah it still doesn't make sense. I have now...0.95 blood match and 0.05 blood not match and then for the second branch of blood match, i have man guilty 0.01 and man not guilty 0.99. do i just write zero for the second branch of blood not match?
From what I understand there is a 1% chance that the blood will match and then if the blood does match there will then be a 0.95 chance of getting a match. If we let A = matches blood and B = matches including degradation we'd get

A' = (1-A) = 0.99
B' = (1-B) = 0.05

P(AB) = 0.01*0.95