Question

1. crimes committed the numbers show the number of crimes committed in a large city. if a crime is selected at random, find the probability that it is a motor vehicle theft. what is the probability that it is not an assault? theft 1375 burglary of home or office 500 motor vehicle theft 275 assault 200 robbery 125 rape or homicide 25 source: based on fbi statistics.

Explanation:

Step1: Calculate total number of crimes

Sum up all the crime numbers: \(1375 + 500+275 + 200+125 + 25\)

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Step2: Calculate probability of motor - vehicle theft

Use the formula \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of motor - vehicle thefts (\(n(A) = 275\)) and \(n(S)\) is the total number of crimes (\(n(S)=2500\)). So \(P(\text{motor - vehicle theft})=\frac{275}{2500}=\frac{11}{100}=0.11\)

Step3: Calculate probability of not an assault

First, find the number of assaults \(n(\text{assault}) = 200\). Then use the formula \(P(\text{not assault})=1 - P(\text{assault})\). \(P(\text{assault})=\frac{200}{2500}=\frac{2}{25}\). So \(P(\text{not assault})=1-\frac{200}{2500}=\frac{2500 - 200}{2500}=\frac{2300}{2500}=\frac{23}{25}=0.92\)

Answer:

The probability that a randomly selected crime is a motor - vehicle theft is \(0.11\). The probability that a randomly selected crime is not an assault is \(0.92\)