EXCELL SPREAD SHEET ANSWER PLEASE!!!! The population of a particular country con

Question

EXCELL SPREAD SHEET ANSWER PLEASE!!!!

The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. Calculate P(A), P(C), and P(A C). Calculate both P(A/C) and P(C/A), and explain in con- text what each of these probabilities represents. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?

Explanation / Answer

a) from above P(A) =0.447

and P(B) =0.091

and probabilty of ethnic group 3 to be selected =P(C)= 0.5

b) P(A|C) =probabilty of type A, given C is selected =0.2/0.5 =2/5 =0.4

P(C|A) =probability of etnic group 3 when type A is selected = 0.2/0.447 =0.4474

c) probabilty of not having type B blood =P(Bc) =1-0.091 =0.909

also probabilty of not having type B blood group and from ethnic group 1 =P(1nBc)=0.2-0.008 =0.192

hence probabilty that from ethnic group 1 , given does not have type B blood =P(1|Bc) =P(1nBc)/P(Bc) =0.192/0.909 =0.2112

Blood Group O A B AB Total Ethnic Group 1 0.082 0.106 0.008 0.004 0.2 2 0.135 0.141 0.018 0.006 0.3 3 0.215 0.2 0.065 0.02 0.5 Total 0.432 0.447 0.091 0.03 1

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