Crime and Orders
1. The central police station 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.
Age (in years) Type of crime under 20 20 to 40 Over 40 Total Violent 27 41 14 82 Nonviolent 12 34 22 68 Total 39 75 36 150
a. What is the probability of selecting a case to analyze and finding it involved a violent crime? = 82/150
b. What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old? = 115/150
c. What is the probability of selecting a case that involved a violent crime or an offender less than 20 years old? Which rule of addition did you apply? = (82+12) /150 = 94/150 This is a (mutually exclusive additional) rule
d. Given that a violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old? = 27/82
e. Two crimes are selected for review by judge Tembo. What is the probability that both are violent crimes? Number of ways to pick 2 crimes order does not matter out of the total 150 crimes:- = 150 = 150. 149. 148 = 22,350 = 11,175 (150-2) 148 (2.1) 2
Number of ways to pick 2 crimes where order does NOT matter and both are violent
= 82 = 82. 81. 80 = 6,642 = 3,321 (82 – 2) 80(2.1) 2
= 3,321/ 11,175 = 0.297 = 29.72 %
2. Accuracy in taking orders at the drive-thru window is an important feature for fast- food chains. Each month QSR magazine publishes the results of its surveys. Accuracy is measured as a percentage of orders consisting of a main
Age (in years) Type of crime under 20 20 to 40 Over 40 Total Violent 27 41 14 82 Nonviolent 12 34 22 68 Total 39 75 36 150
a. What is the probability of selecting a case to analyze and finding it involved a violent crime? = 82/150
b. What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old? = 115/150
c. What is the probability of selecting a case that involved a violent crime or an offender less than 20 years old? Which rule of addition did you apply? = (82+12) /150 = 94/150 This is a (mutually exclusive additional) rule
d. Given that a violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old? = 27/82
e. Two crimes are selected for review by judge Tembo. What is the probability that both are violent crimes? Number of ways to pick 2 crimes order does not matter out of the total 150 crimes:- = 150 = 150. 149. 148 = 22,350 = 11,175 (150-2) 148 (2.1) 2
Number of ways to pick 2 crimes where order does NOT matter and both are violent
= 82 = 82. 81. 80 = 6,642 = 3,321 (82 – 2) 80(2.1) 2
= 3,321/ 11,175 = 0.297 = 29.72 %
2. Accuracy in taking orders at the drive-thru window is an important feature for fast- food chains. Each month QSR magazine publishes the results of its surveys. Accuracy is measured as a percentage of orders consisting of a main