Question 568919: A man claimed not to be the father of a certain child. On the basis of evidence presented, the court felt that this man was twice as likely to be the father as not. The blood type of the child is solely determined by the father, if it did not match the blood type of the child, than he could not be the father. The blood type of the child only occurred in only 10% of the population. The blood test indicated that the man had the same blood type as the child, what is the probability that the man is the father?
Thank You!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i interpret this problem as follows:
On the basis of evidence presented, the court felt that this man was twice as likely to be the father as not.
I read this to mean that the probability that he is the father is 2/3 and the probability that he is not the father is 1/3 because 2/3 is twice the value of 1/3.
that's if blood type is not taken into consideration.
if blood type is taken into consideration, then the likelihood that he is the father becomes 10 times greater because only 10% of the population has the same blood type.
since he is already 2 times as likely to be the father than not, then this means that he becomes 10 times as likely as that which mean that he becomes 20 times as likely to be the father as not.
if he is 20 times as likely as not, then i read this to mean that the probability that he is the father is 20 times the probability that he is not the father.
if we let x equal the probability that he is the father, then 1 - x is the probability that he is not the father.
our equation becomes:
x = 20 * (1 - x)
simplify this to get:
x = 20 - 20x
add 20x to both sides of this equation to get:
21x = 20
divide both sides of this equation by 21 to get:
x = 20/21 = .9523809524 which is equal to 95.24% rounded to 2 decimal places.
the probability that he is the father is 2/3 = 66.67% if blood type is not taken into consideration.
the probability that he is the father is 95.24% if blood type is taken into consideration on top of that.
this assumes my assumptions on how to calculate a problem such as this are correct.
not having done one like this before, my assumptions are speculative.
i tried looking at it other ways but came up empty.
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