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Answer :
In the town of Goslar, the probability that a crime goes unreported is 26%. Assuming a crime is reported, the probability that the crime is violent is approximately 24.3%.
Let's analyze each section separately:
(a) To calculate the probability that a crime goes unreported, we need to find the proportion of crimes that are not reported. We can do this by subtracting the proportion of reported crimes from 1.
The proportion of violent crimes that are reported is 90%, so the proportion of violent crimes that go unreported is 100% - 90% = 10%.
The proportion of nonviolent crimes that are reported is 70%, so the proportion of nonviolent crimes that go unreported is 100% - 70% = 30%.
To calculate the overall probability of a crime going unreported, we need to weight the proportions of unreported crimes by their respective probabilities. Since 20% of all crimes are violent and 80% are nonviolent, we can calculate the overall probability as follows:
(20% * 10%) + (80% * 30%) = 2% + 24% = 26%.
Therefore, the probability that a crime goes unreported in the town of Goslar is 26%.
(b) Assuming a crime is reported, we need to calculate the probability that the crime is violent. This can be done by considering the proportion of reported crimes that are violent out of all reported crimes.
The proportion of violent crimes that are reported is 90%, and the proportion of nonviolent crimes that are reported is 70%. Since the reported crimes consist of both violent and nonviolent crimes, we can calculate the probability as follows:
(90% * 20%) / [(90% * 20%) + (70% * 80%)] = 18% / (18% + 56%) ≈ 18% / 74% ≈ 24.3%.
Therefore, if a crime is reported in the town of Goslar, the probability that it is violent is approximately 24.3%.
To know more about calculating probabilities, refer here:
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