Uncertainty and Probabilistic Reasoning II

• An example of Bayesian reasoning
  You would like to know the chance that it will rain within the next day on a particular planet. You can see that there are green clouds in the sky but no purple clouds. You also know that the chance of rain in general during this season is .1, that when it's raining there have been green clouds in the sky during the past day 60% of the time and purple clouds in the sky 30% of the time, and that when it isn't raining there have been green clouds in the sky during the last day 20% of the time and purple clouds 50% of the time. Calculate the probability that it will rain, making the usual simplifying assumptions. Also explain what these assumptions are.
• Fallacies in human probabilistic judgement (Tversky & Kahneman)
  • Some tests
    1. Which are more frequent, words beginning with the letter 'R' or words in which 'R' is the third letter?
    2. What's the result of the calculation: 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8? (Average response: 512) What's the result of the calculation: 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1? (Average response: 2,250) (Right answer: 40,320).
    3. You are playing roulette and observe the sequence: Red Red Red Red Red. What color should you bet on next?
    4. A certain town has two hospitals: one is large and has about 45 births per day; the other is small and has about 15 births per day. Assuming that boys are equally likely as girls, is there any difference between the hospitals in the number of days on which 60% or more of the babies born are boys?
    5. Bill is 34 years old. He is intelligent, but unimaginative, compulsive, and generally lifeless. In school, he was strong in math but weak in social studies and humanities. How likely would you rate (on a scale of 1 to 7) each of the following propositions?
       1. Bill is an accountant.
       2. Bill is an accountant who plays jazz for a hobby.
       3. Bill is a physician who plays poker for a hobby.
       4. Bill is an architect.
       5. Bill climbs mountains for a hobby.
       6. Bill plays jazz for a hobby.
    6. Which of the following lotteries would you prefer?
       A: 80% chance at $4000
       B: 100% chance at $3000
    7. Which of the following lotteries would you prefer?
       C: 20% chance at $4000
       D: 25% chance at $3000
• Some events are perceived as so unique that past history does not seem relevant to the evaluation of their likelihood. Instead we create scenarios. The plausibility of the scenarios that come to mind, or the difficulty of producing them, serve as clues about the likelihood of the event.
• People are risk-averse with high probability events but are willing to take more risks with unlikely payoffs.