(Solved): 8. Switched-Conditionals Fallacy. If it bleeds, it leads: Nearly \( 60 \% \) ...

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8. Switched-Conditionals Fallacy. If it bleeds, it leads: Nearly \( 60 \% \) of violent crime stories carried in the media show a green fanged alien being handcuffed and escorted into a police car. Assume that (i) \( 57 \% \) of violent criminals are green-fanged aliens (so the media coverage is essentially unbiased); (ii) green-fanged aliens make up only \( 18.7 \% \) of the population; and (iii) \( 0.16 \% \) of the population are violent criminals. A green-fanged alien is seen on the way to the grocery store. What are the chances this alien is a violent criminal? L11. Paradox/Fallacy Exercises 9. Switched-Conditionals Fallacy. There are 100 known terrorists in a city of 1000000 people. To find these terrorists, officials have placed cameras around the city and installed state-of-the-art "facial recognition" software. The software developer claims the recognition software is very accurate. Specifically, if the camera captures a terrorist, there is a \( 99 \% \) chance the software will sound an alarm. If the camera captures a non terrorist, there is a \( 99 \% \) chance the software will not sound an alarm. a) If the alarm sounds, what are the chances the camera has captured a terrorist? b) What are the chances of a false alarm? 10. Simpson's Paradox. Carla and Janice have played together in different softball leagues over the past 4 years. Carla has had a higher batting average in each of the 4 years-see the data below: After hearing enough of Carla's bragging, Janice politely (and happily) points out that she, Janice, actually has the higher overall (4-year) batting average. a) Show that although Carla has had the higher batting average in each of the 4 years, Janice has the higher overall (4-year) batting average. b) Who has bragging rights, Carla or Janice? That is, who is the better hitter (as measured using batting average)? Discuss/debate.