4. Probability
Basic Concepts of Probability
1:07 minutesProblem 14.CRE.1a
Textbook Question
Federal Criminal Defendants The following graph depicts results from a study of defendants in federal crime cases (based on data from the Administrative Office of the U.S. Courts).
a. If a defendant is randomly selected what is the probability that this person had their case dismissed before going to trial?
Verified step by step guidance1
Step 1: Understand the problem. The question asks for the probability that a randomly selected federal criminal defendant had their case dismissed before going to trial. This requires identifying the proportion of defendants whose cases were dismissed from the given data.
Step 2: Analyze the graph. The pie chart shows three categories: 'Pleaded guilty: 90%', 'Had case dismissed: 8%', and 'Went to trial: 2%'. The percentage of cases dismissed is clearly labeled as 8%.
Step 3: Recall the concept of probability. Probability is calculated as the ratio of favorable outcomes to the total number of outcomes. Here, the favorable outcome is the case being dismissed, and the total outcomes are all defendants represented in the chart.
Step 4: Express the probability mathematically. The probability of a case being dismissed is given directly by the percentage in the chart. Convert this percentage into a decimal form for standard probability representation: \( P(\text{case dismissed}) = \frac{8}{100} \).
Step 5: Conclude the steps. The probability that a randomly selected defendant had their case dismissed is equivalent to the decimal representation of 8%, which is \( 0.08 \). No further calculations are needed as the percentage is directly provided in the graph.
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