At a certain stage of a criminal investigation, the inspector in charge is 60 percent convinced of the guilt of a certain suspect. Suppose, however, that a new piece of evidence which shows that the criminal has a certain characteristic (such as left-handedness, baldness, or brown hair) is uncovered. If 20 percent of the population possesses this characteristic, how certain of the guilt of the suspect should the inspector now be if it turns out that the suspect has the characteristic?
Added by Thomas J.
Close
Step 1
6 - Probability of the population possessing the characteristic, P(C) = 0.2 - Probability of having the characteristic given guilt, P(C|G) = 1 We can use Bayes' theorem to find the probability of guilt given the suspect has the characteristic: P(G|C) = P(C|G) * Show more…
Show all steps
Your feedback will help us improve your experience
Kshipra R and 61 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A defendant (suspect) in police custody had clothes that had a victim's DNA after forensic analysis. Using this information only, would you convict the suspect of a crime? A. Absolutely, the suspect is 100% guilty! B. Yes, because there is no other way to explain presence of the victim's DNA in clothes worn by suspect C. Yes, 80% guilty, but would wait for further forensic evidence for the remaining 20% D. No, there is not enough evidence to convict the suspect! E. Unsure - 50% guilty; 50% not guilty!
Andrew M.
A truth serum has the property that 90% of the guilty suspects are properly judged, while, of course, 10% of the guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 1% of the time. If the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent?
Sri K.
Crime: Murder What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About $64 \%$ of people who are murdered actually knew the person who committed the murder (Source: Chances: Risk and Odds in Everyday Life, by James Burke). Suppose that a detective file in New Orleans has 63 current unsolved murders. What is the probability that (a) at least 35 of the victims knew their murderers? (b) at most 48 of the victims knew their murderers? (c) fewer than 30 victims did not know their murderers? (d) more than 20 victims did not know their murderers?
Normal Curves and Sampling Distributions
Normal Approximation to Binomial Distribution and to $\hat{p}$ Distribution
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD