A certain sheriff\'s office classifies crimes committed in the county by the cri

Question

A certain sheriff's office classifies crimes committed in the county by the criminal's age group and the type of crime committed. Last year there were a total of 1000 crimes committed. 150 of these were considered violent crimes where 23 were committed by persons under 20 years of age and 30 were committed by someone older than 40. In the "non-violent" category, 298 and 255 were committed by persons younger than 20 and older than 40 respectively. A) Complete Table 1 by entering the appropriate cell frequencies Given a randomly selected crime record: B) The probability that the crime was committed by a person younger than 20 years old is: C) The probability that the crime was committed by a person who was not younger than 20 years old is: D) The probability that the crime is classified as a violent crime is: E) The probability that the crime was classified as non-violent or was committed by a person in the 20 to 40 year old age group is: F) The probability that the criminal was over 40 given that it was a violent crime is: G) The probability that the criminal was over 40 and that it was classified as a violent crime is: H) The probability that it was a violent crime given that the criminal was over 40 years old is:

Explanation / Answer

Given,

B)The probability that the crime was committed by a person younger than 20 years old is:

= Number crimes committed by persons under age 20 /Total number of crimes committed = 321/1000

probability that the crime was committed by a person younger than 20 years old is = 321/1000

C)The probability that the crime was committed by a person who was not younger than 20 years old is :

probability that the crime was committed by a person who was not younger than 20 years old = 1- probability that the crime was committed by a person younger than 20 years old = 1-321/1000 = (1000-321)/1000 = 679/1000

The probability that the crime was committed by a person who was not younger than 20 years old is = 679/1000

D)The probability that the crime is classified as a violent crime is

= Number of crimes classfied as Violent / Total number of crimes = 150/1000

The probability that the crime is classified as a violent crime is : 150/1000

E)The probability that the crime was classified as a non-violent crime or was committed by a person in 20 to 40 year old age group

= probability that the crime was classified as a non-violent crime + probability that the crime was committed by a person in 20 to 40 year old age group - probability that the crime was classified as a non-violent crime and was cmmitted by 20 to 40 year old age group

probability that the crime was classified as a non-violent crime =  Number of crimes classfied as non-Violent / Total number of crimes = 850/1000

probability that the crime was committed by a person in 20 to 40 year old age group   = Number crimes committed by persons in 20-40 year old age froup /Total number of crimes comiitted = 394/1000

probability that the crime was classified as a non-violent crime and was cmmitted by 20 to 40 year old age group = Number of crimes classified as a non-violent crime and were cmmitted by 20 to 40 year old age group / Total number of crimes = 297/1000

probability that the crime was classified as a non-violent crime + probability that the crime was committed by a person in 20 to 40 year old age group = 850/1000 + 394/1000 -297/1000= (850+394-297)/1000 =947/1000

Under 20 20 to 40 over 40 Total Violent 23 30 150 Non-Violent 298 255 Total 1000

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