1. A theft was committed. It was definitely committed by only one person. It was probably committed by one of the three stooges, Curly Larry, and Moe. Suppose I have the following degrees of confidence in these mutually exclusive and jointly exhaustive hypotheses: Curly did it = .25 Larry did it = 2 Moe did it = .15 none of them did it = .4 Suppose I learn that Larry definitely didn't do it. How confident should I now be that one of the three stooges did it? a. Noelle applied to Southeast Michigan International College (SMIC). The school is very selective and its standards are notoriously secret, and difficult to ascertain. They receive 30,000 applications every year and only admit 30 students per year. She also knows that SMIC acceptance and rejection emails have subject lines with a very particular pattern. 80% of those who are accepted receive an email with a subject line that starts with "Thank you", while 20% of those who are rejected also receive an email with a subject line that starts with "Thank you". One morning, Noelle sees an email from SMIC in her inbox with a subject line starting with "Thank you and screams for joy, concluding that she probably just got an acceptance email from SMIC. A Heads i win; tails we're even B Selective updating o C Base rate neglect O D One-sided strength testing b. Nastas is on a flight from Detroit to Boston when he feels his seat begin to shake. He tries to think back to his critical reasoning section where this example was discussed and remembers something about P(EH). He figures out that, indeed, the plane is very likely to shake if it is about to crash land, and begins to scream in terror. O A Heads I win; tails we're even O B Selective updating C Base rate neglect D One-sided strength testing d. Natalya is a Zoology-Computer Science double major, who is preparing to apply for an internship at a hot, new startup called Snapp3Mapp3, which is developing an app where you can send disappearing directions to exclusive parties. Its steadily growing user base and trendy branding among college students makes it an attractive place to work for ambitious, entrepreneurially-minded young professionals. Snapp3Mapp3 is known for their interest in very-specific college majors, despite the fact that the majority of applicants for their job openings majored exclusively in computer science or marketing. They hire 1% of applicants who majored in Computer Science, 2% of applicants who majored in marketing, but they hire 90% of applicants who majored in zoology, 95% of applicants who majored in astronomy, and 99% of applicants who double majored in zoology or astronomy along with another major. Natalya's arch-rival, Ned, hears about this hiring data and decides to taunt Natalya by pointing out that since she majored in Computer Science, she only has a 1% chance of being hired by Snapp3Mapp3 O A Heads i win; tails we're even Selective updating 0 C Base rate neglect O D One-sided strength testing c. Neil brags to his coworkers about his new trick to drive up sales at the car dealership where they work. He tells his coworkers that he always takes his customers on a test drive route that passes by Michigan Stadium and when they pass it, he tells them, "this car is a real champion Inevitably, according to Neil, the customer buys the car upon return to the dealership. One of his coworkers, Naomi, is skeptical, but asks Neil if she can tag along to see the trick in action. Neil agrees and brings Naomi with him on his next test drive with a customer. He uses the same route and makes the remark as usual, but upon return to the dealership, the customer declines to buy the car. Naomi gleefully points out to Neil that the trick doesn't always work after all. In anger, Neil yells "it doesn't work when someone is watching, but otherwise, it guarantees a sale!" Heads I win; tails we're even Selective updating o C Base rate neglect O D One-sided strength testing 1. A theft was committed. It was definitely committed by only one person. It was probably committed by one of the three stooges, Curly Larry, and Moe. Suppose I have the following degrees of confidence in these mutually exclusive and jointly exhaustive hypotheses: Curly did it = .25 Larry did it = 2 Moe did it = .15 none of them did it = .4 Suppose I learn that Larry definitely didn't do it. How confident should I now be that one of the three stooges did it? a. Noelle applied to Southeast Michigan International College (SMIC). The school is very selective and its standards are notoriously secret, and difficult to ascertain. They receive 30,000 applications every year and only admit 30 students per year. She also knows that SMIC acceptance and rejection emails have subject lines with a very particular pattern. 80% of those who are accepted receive an email with a subject line that starts with "Thank you", while 20% of those who are rejected also receive an email with a subject line that starts with "Thank you". One morning, Noelle sees an email from SMIC in her inbox with a subject line starting with "Thank you and screams for joy, concluding that she probably just got an acceptance email from SMIC. A Heads i win; tails we're even B Selective updating o C Base rate neglect O D One-sided strength testing b. Nastas is on a flight from Detroit to Boston when he feels his seat begin to shake. He tries to think back to his critical reasoning section where this example was discussed and remembers something about P(EH). He figures out that, indeed, the plane is very likely to shake if it is about to crash land, and begins to scream in terror. O A Heads I win; tails we're even O B Selective updating C Base rate neglect D One-sided strength testing d. Natalya is a Zoology-Computer Science double major, who is preparing to apply for an internship at a hot, new startup called Snapp3Mapp3, which is developing an app where you can send disappearing directions to exclusive parties. Its steadily growing user base and trendy branding among college students makes it an attractive place to work for ambitious, entrepreneurially-minded young professionals. Snapp3Mapp3 is known for their interest in very-specific college majors, despite the fact that the majority of applicants for their job openings majored exclusively in computer science or marketing. They hire 1% of applicants who majored in Computer Science, 2% of applicants who majored in marketing, but they hire 90% of applicants who majored in zoology, 95% of applicants who majored in astronomy, and 99% of applicants who double majored in zoology or astronomy along with another major. Natalya's arch-rival, Ned, hears about this hiring data and decides to taunt Natalya by pointing out that since she majored in Computer Science, she only has a 1% chance of being hired by Snapp3Mapp3 O A Heads i win; tails we're even Selective updating 0 C Base rate neglect O D One-sided strength testing c. Neil brags to his coworkers about his new trick to drive up sales at the car dealership where they work. He tells his coworkers that he always takes his customers on a test drive route that passes by Michigan Stadium and when they pass it, he tells them, "this car is a real champion Inevitably, according to Neil, the customer buys the car upon return to the dealership. One of his coworkers, Naomi, is skeptical, but asks Neil if she can tag along to see the trick in action. Neil agrees and brings Naomi with him on his next test drive with a customer. He uses the same route and makes the remark as usual, but upon return to the dealership, the customer declines to buy the car. Naomi gleefully points out to Neil that the trick doesn't always work after all. In anger, Neil yells "it doesn't work when someone is watching, but otherwise, it guarantees a sale!" Heads I win; tails we're even Selective updating o C Base rate neglect O D One-sided strength testing