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1

Thun, M. von. "Probability Theory and Probability Semantics." Australasian Journal of Philosophy 79, no. 4 (2001): 570–71. http://dx.doi.org/10.1080/713659287.

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2

Kiessler, Peter C. "Measure Theory and Probability Theory." Journal of the American Statistical Association 102, no. 479 (2007): 1078. http://dx.doi.org/10.1198/jasa.2007.s207.

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3

Berckmoes, B., R. Lowen, and J. Van Casteren. "Approach theory meets probability theory." Topology and its Applications 158, no. 7 (2011): 836–52. http://dx.doi.org/10.1016/j.topol.2011.01.004.

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4

Lindley, D. V., and Harold Jeffreys. "Theory of Probability." Mathematical Gazette 83, no. 497 (1999): 372. http://dx.doi.org/10.2307/3619118.

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5

Guionnet, Alice, Roland Speicher, and Dan-Virgil Voiculescu. "Free Probability Theory." Oberwolfach Reports 12, no. 2 (2015): 1571–629. http://dx.doi.org/10.4171/owr/2015/28.

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6

Guionnet, Alice, Roland Speicher, and Dan-Virgil Voiculescu. "Free Probability Theory." Oberwolfach Reports 15, no. 4 (2019): 3147–215. http://dx.doi.org/10.4171/owr/2018/53.

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7

Bhat, B. R. "Modern Probability Theory." Biometrics 42, no. 4 (1986): 1007. http://dx.doi.org/10.2307/2530732.

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8

Jeffreys, H., P. A. P. Moran, and C. Chatfield. "Theory of Probability." Biometrics 41, no. 2 (1985): 597. http://dx.doi.org/10.2307/2530899.

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9

Speicher, Roland. "Free Probability Theory." Jahresbericht der Deutschen Mathematiker-Vereinigung 119, no. 1 (2016): 3–30. http://dx.doi.org/10.1365/s13291-016-0150-5.

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10

MTW and Harold Jeffreys. "Theory of Probability." Journal of the American Statistical Association 94, no. 448 (1999): 1389. http://dx.doi.org/10.2307/2669965.

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11

RBL and Boris V. Gnedenko. "Theory of Probability." Journal of the American Statistical Association 94, no. 447 (1999): 990. http://dx.doi.org/10.2307/2670030.

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12

Heyer, H. "ALGEBRAIC PROBABILITY THEORY." Bulletin of the London Mathematical Society 22, no. 5 (1990): 523–24. http://dx.doi.org/10.1112/blms/22.5.523.

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13

Rédei, Miklós, and Stephen Jeffrey Summers. "Quantum probability theory." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38, no. 2 (2007): 390–417. http://dx.doi.org/10.1016/j.shpsb.2006.05.006.

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14

Diederich, Adele. "Projective probability theory." Journal of Mathematical Psychology 58 (January 2014): 55–57. http://dx.doi.org/10.1016/j.jmp.2013.12.003.

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15

Rota, Gian-Carlo. "Algebraic probability theory." Advances in Mathematics 84, no. 2 (1990): 272. http://dx.doi.org/10.1016/0001-8708(90)90050-w.

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16

Lane, John A., and J. Galambos. "Advanced Probability Theory." Applied Statistics 39, no. 2 (1990): 263. http://dx.doi.org/10.2307/2347769.

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17

Davy, P. J., and Janos Galambos. "Introductory Probability Theory." Applied Statistics 36, no. 3 (1987): 376. http://dx.doi.org/10.2307/2347800.

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18

Carlson, Roger, J. Galambos, M. A. Goldberg, et al. "Introductory Probability Theory." Journal of the American Statistical Association 81, no. 396 (1986): 1117. http://dx.doi.org/10.2307/2289097.

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19

Maslov, V. P. "Unbounded probability theory compatible with the probability theory of numbers." Mathematical Notes 91, no. 5-6 (2012): 697–703. http://dx.doi.org/10.1134/s0001434612050112.

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20

Erkinovna, Ergasheva Fatima, and Egamberdiyeva Mohinur Fakhriddin kizi. "OTHER METHODS OF TEACHING PROBABILITY THEORY AND COMBINATORICS." American Journal of Applied Sciences 6, no. 3 (2024): 13–15. http://dx.doi.org/10.37547/tajas/volume06issue03-03.

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The traditional methods of teaching probability theory and combinatorics often fail to engage students and promote deep understanding. This study explores alternative teaching strategies that incorporate active learning, technology, and real-world applications to enhance student comprehension and interest in these mathematical fields. By comparing the effectiveness of these methods with conventional approaches, this research aims to provide educators with practical insights for improving mathematics education.
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21

Clarke, L. E., Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Mathematical Gazette 71, no. 455 (1987): 80. http://dx.doi.org/10.2307/3616316.

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22

Rosalsky, Andrew, Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Journal of the American Statistical Association 82, no. 398 (1987): 700. http://dx.doi.org/10.2307/2289512.

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23

Prewitt, Kathryn, and Richard Durrett. "Probability: Theory and Examples." Journal of the American Statistical Association 87, no. 418 (1992): 586. http://dx.doi.org/10.2307/2290301.

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24

RL, Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Journal of the American Statistical Association 91, no. 436 (1996): 1754. http://dx.doi.org/10.2307/2291614.

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25

Durrett, R. "Probability: Theory and Examples." Biometrics 49, no. 3 (1993): 959. http://dx.doi.org/10.2307/2532227.

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26

Hirst, K. E., and E. A. Robinson. "Probability Theory and Application." Mathematical Gazette 70, no. 454 (1986): 321. http://dx.doi.org/10.2307/3616216.

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27

Kendall, Wilfrid S. "INTRODUCTION TO PROBABILITY THEORY." Bulletin of the London Mathematical Society 17, no. 6 (1985): 601–3. http://dx.doi.org/10.1112/blms/17.6.601.

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28

Rogers, L. C. G. "PROBABILITY: THEORY AND EXAMPLES." Bulletin of the London Mathematical Society 24, no. 2 (1992): 205–6. http://dx.doi.org/10.1112/blms/24.2.205.

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29

Kolmogorov, A. N. "Problems of Probability Theory." Theory of Probability & Its Applications 38, no. 2 (1994): 177–78. http://dx.doi.org/10.1137/1138020.

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30

Frigg, Roman, and Carl Hoefer. "Probability in GRW theory." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38, no. 2 (2007): 371–89. http://dx.doi.org/10.1016/j.shpsb.2006.12.002.

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31

Rota, Gian-Carlo. "Elements of probability theory." Advances in Mathematics 55, no. 1 (1985): 101. http://dx.doi.org/10.1016/0001-8708(85)90008-8.

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32

Drummond-Cole, Gabriel C., Jae-Suk Park, and John Terilla. "Homotopy probability theory I." Journal of Homotopy and Related Structures 10, no. 3 (2013): 425–35. http://dx.doi.org/10.1007/s40062-013-0067-y.

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33

Drummond-Cole, Gabriel C., Jae-Suk Park, and John Terilla. "Homotopy probability theory II." Journal of Homotopy and Related Structures 10, no. 3 (2014): 623–35. http://dx.doi.org/10.1007/s40062-014-0078-3.

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34

Athreya, K. B. "What is probability theory?" Resonance 20, no. 4 (2015): 292–310. http://dx.doi.org/10.1007/s12045-015-0186-3.

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35

Bru, Bernard. "Lagrange and probability theory." Lettera Matematica 2, no. 1-2 (2014): 67–74. http://dx.doi.org/10.1007/s40329-014-0047-z.

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36

Schlechta, Karl. "Theory revision and probability." Notre Dame Journal of Formal Logic 32, no. 2 (1991): 307–19. http://dx.doi.org/10.1305/ndjfl/1093635755.

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37

Snell, J. Laurie, and Kiyosi Ito. "Introduction to Probability Theory." Journal of the American Statistical Association 81, no. 395 (1986): 857. http://dx.doi.org/10.2307/2289022.

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38

Mittal, Yashaswini, and M. M. Rao. "Probability Theory With Applications." Journal of the American Statistical Association 81, no. 394 (1986): 579. http://dx.doi.org/10.2307/2289275.

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39

Marletto, Chiara. "Constructor theory of probability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2192 (2016): 20150883. http://dx.doi.org/10.1098/rspa.2015.0883.

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Unitary quantum theory, having no Born Rule, is non-probabilistic . Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalizing and improving upon the so-called ‘decision-theoretic approach’, I shall recast that problem in the recently proposed constructor theory of information— where quantum theory is represented as one of a class of superinformation theories , which are local , non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement out
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40

Currie, Iain D., and E. A. Robinson. "Probability Theory and Applications." Journal of the Royal Statistical Society. Series A (General) 149, no. 3 (1986): 278. http://dx.doi.org/10.2307/2981570.

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41

Kennedy, D. P., and Kiyosi Ito. "Introduction to Probability Theory." Journal of the Royal Statistical Society. Series A (General) 148, no. 3 (1985): 283. http://dx.doi.org/10.2307/2981977.

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42

REEVES, T. V. "A Theory of Probability." British Journal for the Philosophy of Science 39, no. 2 (1988): 161–82. http://dx.doi.org/10.1093/bjps/39.2.161.

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43

JANSONS, KALVIS M., and L. C. G. ROGERS. "Probability and dispersion theory." IMA Journal of Applied Mathematics 55, no. 2 (1995): 149–62. http://dx.doi.org/10.1093/imamat/55.2.149.

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44

Maslov, V. P. "On unbounded probability theory." Mathematical Notes 92, no. 1-2 (2012): 59–63. http://dx.doi.org/10.1134/s0001434612070073.

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45

Spouge, John L. "Introduction to probability theory." Mathematical Biosciences 78, no. 2 (1986): 311. http://dx.doi.org/10.1016/0025-5564(86)90132-x.

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46

Bagwell, C. Bruce, Benjamin C. Hunsberger, Donald J. Herbert, et al. "Probability state modeling theory." Cytometry Part A 87, no. 7 (2015): 646–60. http://dx.doi.org/10.1002/cyto.a.22687.

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47

Kolmogorov, A. N., and S. Natarajan. "The theory of probability." Resonance 3, no. 4 (1998): 103–12. http://dx.doi.org/10.1007/bf02834617.

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48

Shiryaev, A. N. "Chair of Probability Theory." Moscow University Mathematics Bulletin 79, no. 6 (2024): 343–50. https://doi.org/10.3103/s0027132225700111.

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49

Golomb, Solomon W. "Probability, information theory, and prime number theory." Discrete Mathematics 106-107 (September 1992): 219–29. http://dx.doi.org/10.1016/0012-365x(92)90549-u.

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50

Diecidue, Enrico, Haim Levy, and Moshe Levy. "Probability Dominance." Review of Economics and Statistics 102, no. 5 (2020): 1006–20. http://dx.doi.org/10.1162/rest_a_00890.

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The most commonly employed paradigms for decision making under risk are expected utility, prospect theory, and regret theory. We examine the simple heuristic of maximizing the probability of being ahead, which in some natural economic situations may be in contradiction to all three of the above fundamental paradigms. We test whether this heuristic, which we call probability dominance (PD), affects decisions under risk. We set up head-to-head situations where all preferences of a given class (expected utility, original or cumulative prospect theory, or regret theory) favor one alternative yet P
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