The Wood Country Sheriff Classifies crimes by age (in years) of the criminal and

Question

The Wood Country Sheriff Classifies crimes by age (in years) of the criminal and whether the crime is violent or nonviolent. As shown below, a total of 150 crimes were reported by the sheriff last year.

A. What is the possibility of selecting a case to analyze and finding it involved a violent crime?

B. What is the possibility of selecting a case to analyze abd finding the crime was committed by someone less than 40 years old?

C. What is the possibility of selecting a case that involved a violent crime of an offended less than 20 years old?

D. Given that the violent crime is slelected for analysis, what is the probability the crime was commited by a person under 20 years old?

E. Two crimes are selected by Judge Tybo. What is the probablility both are violent crimes?

Please show all work for the above questions.

Thanks

Explanation / Answer

a) the probability of selecting a violent case out of the 150 total when selecting 1 case = 82/150

b) the probability the 1 case you choose involves someone under 40 = (39 + 75) / 150

c)- violent crime AND/OR an offender under 20 =(82+12)/150
-violent crime OR ( no under 20 violentcrimes count as they are not an OR statement....they are an AND statement )
= (12 + 82 - 27)/150

d) probability of a violent crime being committed by someone under 20 = 27/82

e) probability BOTH crimes selected are violent crimes
= (82_C_2) ( number of ways to pick 2 crimes where order does NOT matter and both are violent) / (150_C_2) ( number of ways to pick 2 crimes order does not matter out of the total 150 crimes )
= 3321/11175 = 29.718% = 29.72%

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