You are assigned to the jury of a paternity case; determining whether the the child's guardian father is actually his biological father. After listening to all the witnesses regarding the child's family, you are 75% convinced that the guardian father is the child's biological father. Additionally, you have been presented with laboratory blood tests indicating that the child has blood type B. The laboratory further provided population statistics stating that (a) If the guardian father is assumed to be the biological father, the child has 50% chance of having blood type B. (b) If the guardian father is assumed to NOT be the biological father, the child has 0.91% chance to have a blood type OTHER than B. How confident are you (what is the probability) that the guarding father is the child's biological father

Question

Finnegan Waller

Mathematics

7 May, 14:12

You are assigned to the jury of a paternity case; determining whether the the child's guardian father is actually his biological father. After listening to all the witnesses regarding the child's family, you are 75% convinced that the guardian father is the child's biological father. Additionally, you have been presented with laboratory blood tests indicating that the child has blood type B. The laboratory further provided population statistics stating that (a) If the guardian father is assumed to be the biological father, the child has 50% chance of having blood type B. (b) If the guardian father is assumed to NOT be the biological father, the child has 0.91% chance to have a blood type OTHER than B. How confident are you (what is the probability) that the guarding father is the child's biological father

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Answers (1)

Know the Answer?

Raymond · Answer 1

Answer: 0.6022

Consider the following calculation

Step-by-step explanation:

Let F shows the event that guardian father is biological father. So

P (F) = 0.75

By the complement rule,

P (F') = 1 - P (F) = 1 - 0.75 = 0.25

Let B shows the event that child has blood type B. So we have

P (B|F) = 0.50, P (B' |F') = 0.0091

By the complement rule we have

P (B|F') = 1 - P (B' |F') = 0.9909

The probability that the guarding father is the child's biological father given that child have blood type B is

P (BFPF) P (F|B) = PRI P (BF) P (F) + P (BF) P (F) 0.50 - 0.75 0.50 - 0.75 + 0.9909 - 0.25

0.375 0.622725 = 0.6022

Answer: 0.6022