Police Complaints The Chicago Tribune analyzed 17,713 complaints by citizens against Chicago police officers.
a. Of the 17,713 complaints against police officers, it was found that 7296 were accompanied by a signed affidavit, which is required by state law for the complaint against the officer to proceed. What is the probability that a randomly selected complaint is accompanied by a signed affidavit?

Verified step by step guidance

1. Identify the total number of complaints, which is 17,713, and the number of complaints accompanied by a signed affidavit, which is 7,296.
2. Recall that the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
3. Set up the probability formula for the event "complaint accompanied by a signed affidavit" as: \(P = \frac{\text{Number of complaints with affidavit}}{\text{Total number of complaints}}\).
4. Substitute the given values into the formula: \(P = \frac{7296}{17713}\).
5. Interpret the result as the probability that a randomly selected complaint is accompanied by a signed affidavit.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this question, the probability is the ratio of complaints with signed affidavits to the total complaints.

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. Here, the sample space consists of all 17,713 complaints filed against police officers. Understanding the sample space is essential to correctly calculate probabilities.

Event

An event is a specific outcome or a set of outcomes within the sample space. In this problem, the event is selecting a complaint that includes a signed affidavit. Identifying the event helps focus the probability calculation on relevant data.