Worksheet 8: Common mistakes in conditional logic

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Base rate fallacy.

1. Why is the “false positive test” scenario an example of the base rate fallacy? \vspace{37mm}

2. Why is the “personality traits” example an example of the base rate fallacy? \vspace{37mm}

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?

5. Phrase this question in the language of conditional probabilities. \vspace{37mm}

6. Does being from California increase or decrease your chances of playing in the NFL? \vspace{37mm}

7. What is wrong with the reasoning in the “Scottish hikers” example? Phrase it in the language of conditional probability. \vspace{37mm}

The prosecutor’s fallacy.

8. In the Sally Clark example, what does the 1/73 million calculation assume? What’s wrong with this assumption? \vspace{37mm}

9. What is the problem with the conditional logic applied by the prosecution? \vspace{37mm}

The defense attorney’s fallacy.

10. Why is the “qualifying exam” example an example of the defense attorney’s fallacy? Put it in the language of conditional probabilities. \vspace{37mm}

Sample bias.

11. Put the “hot guys are jerks” example into the language of conditonal probabilities. \vspace{37mm}