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On a Problem in Conditional Probability

Published online by Cambridge University Press:  14 March 2022

A. I. Dale
A. I. Dale*
Affiliation:
University of Natal
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Extract

In an article “Countering a Counter-intuitive Probability” [4], Lynn E. Rose discusses a question in conditional probability, claiming that the following problem posed by Copi [1] is usually incorrectly solved:

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 his cards and announces (truthfully) that his hand contains an ace, what is the probability that both his cards are aces? If he announces instead that one of his cards is the ace of spades, what is the probability then that both his cards are aces? (These two probabilities are not the same!) ([1], p. 433)

Type
Discussion
Information
Philosophy of Science , Volume 41 , Issue 2 , June 1974 , pp. 204 - 206
Copyright
Copyright © 1974 by The Philosophy of Science Association

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References

REFERENCES

[1] Copi, I. M. Introduction to Logic, New York: Macmillan, 1968Google Scholar
[2] Feller, W. An Introduction to Probability Theory and its Applications. New York: Wiley, 1957Google Scholar
[3] Gardner, M. More Mathematical Puzzles and Diversions. London: Bell & Sons, 1963.Google Scholar
[4] Rose, L. E. “Countering a Counter-intuitive Probability.” Philosophy of Science 39 (1972): 523–524.CrossRefGoogle Scholar
[5] Uspensky, J. V. Introduction to Mathematical Probability. New York: McGraw-Hill, 1937.Google Scholar