A closer look at the probabilities of the notorious three prisoners

@article{Falk1992ACL,
  title={A closer look at the probabilities of the notorious three prisoners},
  author={Ruma Falk},
  journal={Cognition},
  year={1992},
  volume={43},
  pages={197-223}
}
  • R. Falk
  • Published 31 December 1992
  • Psychology
  • Cognition
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References

SHOWING 1-10 OF 36 REFERENCES
A paradox of confirmation
Two out of three prisoners, a, b and c, are to be exiled, while the third goes free. The choice of the two has been determined by a fair draw, of whose outcome they are ignorant. Prisoner a is keen
The Taming of Chance.
Acknowledgements 1. The argument 2. The doctrine of necessity 3. Public amateurs, secret bureaucrats 4. Bureaux 5. The sweet despotism of reason 6. The quantum of sickness 7. The granary of science
On the psychology of prediction
In this paper, we explore the rules that determine intuitive predictions and judgments of confidence and contrast these rules to the normative principles of statistical prediction. Two classes of
Presentation and content: The use of base rates as a continuous variable.
Do subjects, in probability revision experiments, generally neglect base rates due to the use of a representativeness heuristic, or does the use of base rates depend on what we call the internal
Re-Encountering a Counter-Intuitive Probability
Remove all cards except aces and kings from a deck, so that only eight cards remain, of which four are aces and four are kings. From this abbreviated deck, deal two cards to a friend. If he looks at
The Emergence of Probability
The Greeks discussed randomness in a qualitative way: Democritus (460BC), Epicurus (341BC) … Yet, mathematical theory of probability came very late:-Gerolamo Cardano (b. 1501, Pavia); Ars Magna
...
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