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Anarel [89]
3 years ago
7

A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of the suspects. After fur

ther investigation, it is determined that the guilty party has a blood type found in only 10% of the population at large. Suspect A does have this blood type; the blood type of Suspect B is unknown.
Define the following 3 events A, M and C.
A: "A is guilty" (Thus ° denotes "B is guilty')
M: "A’s blood type matches that of the guilty party"
C: "B's blood type matches that of the guilty party"
A. The police reported that suspect A is not a relative of suspect B. Is it reasonable to set P( MA)=P(C|A)=10%? Why?
B. Assume that P(MAC)=P(C|A)=10%. Given the information from the further investigation of the crime scene, what is the probability that A is the guilty party?
C. Assume that P( MA)=P(C/A)=10%. Given the information from the further investigation of the crime scene, what is the probability that B’s blood type matches that of the guilty party?
Mathematics
1 answer:
liberstina [14]3 years ago
6 0

Answer:

a) MA conditional with C can be interpreted as A which is known and C which is unknown match

b) 10/11

c) 2/11

Step-by-step explanation:

A={A is the guilty party}

M_A = {A blood type matches that of the guilty party}

C = {B is the guilty party}

M_C = {B blood type matches that of the guilty party}

a) The chance is 10% because MA conditional with C can be interpreted as A which is known and C which is unknown match

b) the probability that A is the guilty party is given by P(A/M_A). Using bayes theorem:

P(A/M_A)=\frac{P(M_A/A)P(A)}{P(M_A/A)P(A)+P(M_C/C)P(C)} =\frac{1*1/2}{(1*1/2)+(1/10*1/2)} =\frac{10}{11}

c) the probability that B’s blood type matches that of the guilty party is given as P(M_C/M_A). Using LOTS Therefore:

P(M_C/M_A)=P(M_C/M_A,A)P(A/M_A)+P(M_C/M_A,A)P(C/M_A)=\frac{1}{10}*\frac{10}{11}  +1*\frac{1}{11}  =\frac{2}{11}

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