Bertrand's chord, Buffon's needle, and the concept of randomness

References

• Ayton , P. , Hunt , A. J. and Wright , G. 1989 . Psychological conceptions of randomness . Journal of Behavioral Decision Making , 2 : 221 – 238 .
   Google Scholar
• Ayton , P. , Hunt , A. J. and Wright , G. 1991 . Randomness and reality, Reply (to comments on “Psychological conceptions of randomness”) . Journal of Behavioral Decision Making , 2 : 222 – 226 .
   Google Scholar
• Baddeley , A. D. 1966 . The capacity for generating information by randomization . Quarterly Journal of Experimental Psychology , 18 : 119 – 129 .
   PubMed Web of Science ®Google Scholar
• Bar-Hillel , M. A. and Falk , R. 1982 . Some teasers concerning conditional probabilities . Cognition , 11 : 109 – 122 .
   PubMed Web of Science ®Google Scholar
• Bar-Hillel , M. A. and Wagenaar , W. A. 1991 . The perception of randomness . Advances in Applied Mathematics , 12 : 428 – 454 .
   Web of Science ®Google Scholar
• Breiman , L. 1969 . Probability and stochastic processes: With a view toward applications , New York : Houghton Mifflin .
   Google Scholar
• Chapanis , A. 1953 . Random number guessing . American Psychologist , 8 : 332
   Google Scholar
• Chung , K. L. 1974 . Elementary probability theory with stochastic processes , New York : Springer-Verlag .
   Google Scholar
• Falk , R. 1975 . Perception of randomness , Jerusalem, , Israel : Hebrew University . Unpublished doctoral dissertation, (in Hebrew, with English abstract)
   Google Scholar
• Falk , R. 1992 . A closer look at the probabilities of the notorious three prisoners . Cognition , 43 : 197 – 223 .
   PubMed Web of Science ®Google Scholar
• Falk , R. 1993 . Understanding probability and statistics: A book of problems , Wellesley, MA : A. K. Peters .
   Google Scholar
• Falk , R. and Konold , C. 1997 . Making sense of randomness: Implicit encoding as a basis for judgment . Psychological Review , 104 : 301 – 318 .
   Web of Science ®Google Scholar
• Feller , W. 1966 . An introduction to probability theory and its applications , Volume 2 , New York : Wiley .
   Google Scholar
• Gardner , M. 1961 . The second Scientific American book of mathematical puzzles and diversions , New York : Simon & Schuster .
   Google Scholar
• Geller , M. J. and Huchra , J. P. 1989 . Mapping the universe . Science , 246 : 897 – 903 .
   PubMed Web of Science ®Google Scholar
• Gnedenko , B. V. 1962 . The theory of probability , New York : Chelsea Publishing . Trans. B. D. Seckler
   Google Scholar
• Kareev , Y. 1992 . Not that bad after all: Generation of random sequences . Journal of Experimental Psychology: Human Perception and Performance , 18 : 1189 – 1194 .
   Web of Science ®Google Scholar
• Kareev , Y. 1995 . Positive bias in the perception of covariation . Psychological Review , 102 : 490 – 502 .
   Web of Science ®Google Scholar
• Lacey , O. L. 1962 . The human organism as a random mechanism . The Journal of General Psychology , 66 : 321 – 325 .
   PubMed Web of Science ®Google Scholar
• Lakatos , I. 1976 . Proofs and refutations: The logic of mathematical discovery , Edited by: Worrall , J. and Zahar , E. New York : Cambridge University Press .
   Google Scholar
• Levy , H. and Roth , L. 1936 . Elements of probability , London : Oxford University Press .
   Google Scholar
• Lisanby , S. H. and Lockhead , G. R. 1991 . “ Subjective randomness, aesthetics, and structure ” . In The perception of structure: Essays in honor of Wendell R. Garner , Edited by: Lockhead , G. R. and Pomerantz , J. R. Washington, DC : American Psychological Association .
   Google Scholar
• Lopes , L. L. 1982 . Doing the impossible: A note on induction and the experience of randomness . Journal of Experimental Psychology: Learning, Memory, and Cognition , 8 : 626 – 636 .
   Web of Science ®Google Scholar
• Mosteller , F. 1965 . Fifty challenging problems in probability with solutions , Reading, MA : Addison-Wesley .
   Google Scholar
• Newman , E. B. and Collier , N. 1952 . Guessing sequences using two, four, and eight alternatives . American Psychologist , 7 : 272 – 273 .
   Google Scholar
• Nickerson , R. S. 1996 . Ambiguities and unstated assumptions in probabilistic reasoning . Psychological Bulletin , 120 : 410 – 433 .
   Web of Science ®Google Scholar
• Nickerson , R. S. 2002 . The production and perception of randomness . Psychological Review , 109 : 330 – 357 .
   PubMed Web of Science ®Google Scholar
• Psotka , J. 1978 . Perceptual processes that may create stick figures and balance . Journal of Experimental Psychology: Human Perception and Performance , 4 : 101 – 111 .
   PubMed Web of Science ®Google Scholar
• Rabinowitz , F. M. 1970 . Characteristic sequential dependencies in multiple-choice situations . Psychological Bulletin , 74 : 141 – 148 .
   Web of Science ®Google Scholar
• Rapoport , A. and Budescu , D. V. 1992 . Generation of random series in two-person strictly competitive games . Journal of Experimental Psychology: General , 121 : 352 – 363 .
   Web of Science ®Google Scholar
• Rapoport , A. and Budescu , D. V. 1997 . Randomization in individual choice behavior . Psychological Review , 104 : 603 – 617 .
   Web of Science ®Google Scholar
• Ross , B. M. and Levy , N. 1958 . Patterned prediction of chance events by children and adults . Psychological Reports , 4 : 87 – 124 .
   Web of Science ®Google Scholar
• Shiryayev , A. N. 1984 . Probability , New York : Springer-Verlag . Trans. R. P. Boss
   Google Scholar
• Slak , S. and Hirsch , K. A. 1974 . Human ability to randomize sequences as a function of information per item . Bulletin of the Psychonomic Society , 4 : 29 – 30 .
   Google Scholar
• Slak , S. , Hirsch , K. A. and Syrja , K. V. 1979 . Randomization of univariate and bivariate sequences and Baddeley's limited capacity hypothesis . Journal of Psychology , 103 : 169 – 182 .
   Web of Science ®Google Scholar
• Solomon , F. 1987 . Probability and stochastic processes , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Stirzaker , D. 1994 . Elementary probability , Cambridge : Cambridge University Press .
   Google Scholar
• Székely , G. J. 1986 . Paradoxes in probability theory and mathematical statistics , Dordrecht : D. Reidel Publishing .
   Google Scholar
• Teraoka , T. 1963 . Some serial properties of “subjective randomness . Japanese Psychological Research , 5 : 120 – 128 .
   Google Scholar
• Todhunter , I. 1949 . A history of the mathematical theory of probability from the time of Pascal to that of LaPlace , New York : Chelsea Publishing Company .
   Google Scholar
• Troccolo , J. A. 1977 . Randomness in physics and mathematics . Mathematics Teacher , 70 : 772 – 774 .
   Google Scholar
• Tuckwell , H. C. 1988 . Elementary applications of probability theory , New York : Chapman & Hall .
   Google Scholar
• Tune , G. S. 1964 . A brief survey of variables that influence random generation . Perceptual and Motor Skills , 18 : 705 – 710 .
   PubMedGoogle Scholar
• Uspensky , J. V. 1937 . Introduction to mathematical probability , New York : McGraw-Hill .
   Google Scholar
• Von Mises , R. 1964 . Mathematical theory of probability and statistics , Edited by: Geiringer , H. New York : Academic Press . edited & complemented by
   Google Scholar
• Wadsworth , G. P. and Bryan , J. G. 1960 . Introduction to probability and random variables , New York : McGraw-Hill .
   Google Scholar
• Wagenaar , W. A. 1970 . “ Subjective randomness and the capacity to generate information ” . In Attention and Performance III , Acta Psychologica, 33 Edited by: Sanders , A. F. 233 – 242 .
   Google Scholar
• Warren , R. A. and Morin , R. E. 1965 . Random generation: Number of symbols to be randomized and time per response . Psychonomic Science , 3 : 557 – 558 .
   Google Scholar
• Weatherford , R. 1982 . Philosophical foundations of probability theory , London : Routledge & Kegan Paul .
   Google Scholar
• Weiss , R. L. 1964 . On producing random sequences . Psychological Reports , 14 : 931 – 941 .
   Web of Science ®Google Scholar
• Weiss , R. L. 1965 . Variables that influence random generation: An alternative hypothesis . Perceptual and Motor Skills , 20 : 307 – 310 .
   PubMed Web of Science ®Google Scholar
• Wiegersma , S. 1982a . A control theory of sequential response production . Psychological Research , 44 : 175 – 188 .
   Web of Science ®Google Scholar
• Wiegersma , S. 1982b . Sequential response bias in randomized response sequences: A computer simulation . Acta Psychologica , 52 : 249 – 256 .
   Web of Science ®Google Scholar