Worksheet 8: Common mistakes in conditional logic

Worksheet 8: Common mistakes in conditional logic#

Your name:

Your student ID number:

Base rate fallacy.

  1. Why is the “false positive test” scenario an example of the base rate fallacy?

  2. Why is the “personality traits” example an example of the base rate fallacy?

Conditional probability out of context.

You are told that the state home to the second-largest number of NFL players is California; 151 out of 1696 players are from California (about 9%). Does being from California improve your chances of playing in the NFL?

  1. Phrase this question in the language of conditional probabilities.

  2. Does being from California increase or decrease your chances of playing in the NFL?

  3. What is wrong with the reasoning in the “Scottish hikers” example? Phrase it in the language of conditional probability.

The prosecutor’s fallacy.

  1. In the Sally Clark example, what does the 1/73 million calculation assume? What’s wrong with this assumption?

  2. What is the problem with the conditional logic applied by the prosecution?

The defense attorney’s fallacy.

  1. Why is the “qualifying exam” example an example of the defense attorney’s fallacy? Put it in the language of conditional probabilities.

Sample bias.

  1. Put the “hot guys are jerks” example into the language of conditonal probabilities.