5. Once in the night, a speeding taxi struck a man as he crossed the street. An eyewitness has testified that she thought the taxi (which did not stop) was blue. The man sued the Blue cab company for his medical expenses. The city where the accident occurred has only two taxi companies: Blue cab and Green cab. Green cab has 85 percent of the taxis' in the city. At the trial, the man's lawyer shows that the eyewitness is 80 percent reliable in identifying the color of taxis. That is, she was able to identify correctly the color of taxis 80 percent of the time, under conditions like those of the night accident. The lawyer concludes that it is extremely likely that a Blue Cab was hit the man. Do you agree? Why or Why not?
Added by Savannah S.
Close
Your feedback will help us improve your experience
Samuel Smith and 66 other Physics 101 Mechanics 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
In a city with one hundred taxis, 1 is blue and 99 are green. A witness observes a hit-and-run by a taxi at night and recalls that the taxi was blue, so the police arrest the blue taxi driver who was on duty that night. The driver proclaims his innocence and hires you to defend him in court. You hire a scientist to test the witness’ ability to distinguish blue and green taxis under conditions similar to the night of accident. The data suggests that the witness sees blue cars as blue 99% of the time and green cars as blue 2% of the time. Write a speech for the jury to give them reasonable doubt about your client’s guilt. Your speech should not be longer than a page. Keep in mind that most jurors have not taken a probability course, so maybe you can use an illustration instead of just formulae
Samuel S.
Two Competing Companies In a certain town, there are two competing taxicab companies, Red Cab and Blue Cab. The taxis mix with downtown traffic in a random manner. There are three times as many Red taxis as there are Blue taxis. Suppose that you stand on a downtown street corner and count the number $X$ of Red taxis that appear before the first Blue taxi appears. (a) Determine the formula for $\operatorname{Pr}(X=n).$ (b) What is the likelihood of observing at least three Red taxis before the first Blue taxi? (c) What is the average number of consecutive Red taxis prior to the appearance of a Blue taxi?
Probability and Calculus
Poisson and Geometric Random Variables
You have been hired as an expert witness for an attorney who is representing a speeding driver. The driver of the car was given a ticket for running a red light at an intersection. According to the driver, who has taken some courses in physics, when he was looking at the red light as he approached the intersection, the Doppler shift made the light of wavelength $650 \mathrm{nm}$ appear to be green light of wavelength $520 \mathrm{nm} .$ Therefore, according to the driver, he should not be charged with running a red light because it appeared green to him. What advice do you give the attorney?
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD