3.74 Identity theft is a growing problem in the United States. According to a Fe
ID: 3307052 • Letter: 3
Question
3.74 Identity theft is a growing problem in the United States. According to a Federal Trade Commission Re- port about 280,000 identity complaints were filed for 2011. Among the 43.2 million persons in the 20-29 year old age group, 56,689 complaints were filed. The 20-29 year old age group makes up proportion .139 of the total population. Use the relative frequencies to approximate the probability, that for the current year, (a) a person in the 20-29 age group files an identity theft complaint (b) a person not in the 20-29 age group files an iden- tity theft complaint. Comment on your answers to Parts (a) and (b). (c) a random person will file an identity theft com- plaint. (d) If a complaint is filed, what is the probability it was by someone in the 20-29 age group.Explanation / Answer
probability that a person in age group 20-29 =P(A) =0.139
let probability of complaint to be filed=P(B)
a) probability that a compaint is filed given person is in 20-29 years of age P(B|A)=56689/(43.2*106) =0.0013
b) number of people not in 20-29 age group =43.2*106*(1-0.139)/0.139=267.59*106
number of complaints not by 20-29 years of age =280000-56689=223311
probability that a person not in the 20-29 age group files an complaint P(B|Ac) =(223311/(267.59*106)) =0.0008
c)probability of filing a complaint =P(B) =P(A)*P(B|A)+P(Ac)*P(B|Ac) =0.139*0.0013+(1-0.139)*0.0008=0.0009
d) probability of complaint by a 20-29 age group person given complaint is filed
=P(A|B) =P(A)*P(B|A)/P(B) =0.139*0.0013/0.0009 =0.2025
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