Prakash Gorroochurn, Ph.D.

Columbia University, Department of Biostatistics

722 W 168th Street, New York, NY 10032

email : [email protected]

phone: 212-342-1263

fax: 212-305-9408

CV (pdf)


Book Chapter

New Book

Japanese Translation of Classic Problems of Probability


Book Interview









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Browse Through the Book

Amazon Link to Book

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Amazon link to Book






I am an Associate Professor in the Department of Biostatistics at Columbia University. I obtained my Ph.D. in Mathematical Population Genetics from Monash University, Australia, in 1999. I am Associate Editor of the journals The American Statistician and BMC Genetics. My main areas of research interest include mathematical population genetics, genetic epidemiology, and the history of probability and statistics.

I am also the author of the book “Classic Problems of Probability” which won the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence





“Classic Problems of Probability” is the winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence.


From the Back Cover

"A great book, one that I will certainly add to my personal library."

—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire


Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature.


From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include:

·        Buffon's Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invariance

·        Various paradoxes raised by Joseph Bertrand

·        Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem

·        The Bayesian paradigm and various philosophies of probability

·        Coverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady tasting tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox

Classic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.


Book Reviewed by Andrew Dale

Book Reviewed by Uwe Küchler



Errata(pdf): Many of the corrections in the attached have already been made in the second printing of the book. Please email me at [email protected] if you notice further errors.





Errors of Probability in Historical Context. In ‘The Best Writings on Mathematics 2013,’ edited by M. Pitici, Princeton University Press (2014). (pdf)



The sequel to “Classic Problems of Probability” is entitled “Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times”. Here is the Table of Contents.(TOC) 


From the Back Cover:

 “There is nothing like it on the others are as encyclopedic...the writing is exemplary:  simple, direct, and competent.”

— George Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College.


Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200 year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics.


Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author deals with post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features:

       A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t

       A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912

       Significant coverage of Neyman-Pearson theory, which includes a discussion of the differences to Fisher’s works

       Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment 

Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.

Book Reviewed by Joel Haack (pdf)

Book Reviewed by Daniel Courgeau (pdf)

Book Reviewed by Christopher J Phillips (pdf)

Book Reviewed by John Haigh (pdf)


My interview on Classic Topics at:


Japanese Translation of “Classic Problems of Probability”

A Japanese translation of “Classic Problems of Probability” was published in Aug 2018 by Kyoritsu Publishing.


A Japanese translation of “Classic Topics on the History of Modern Mathematical Statistics” will be released soon.



1. Gorroochurn, P (2001) Post-Data Inference of Coalescence Times and Segregating-Site Distribution in a Two-Island Model with Symmetric Migration. Advances in Applied Probability 33(3): 600-616.


2. Gorroochurn, P (2001) Genetic Differentiation and Mean Coalescence Times in Two Colonies with Asymmetric Migration. University of Mauritius Research Journal 8: 103-118.

3. Gorroochurn, P (2003) A Note on the Stationary Distribution of an Infinitesimal Matrix. The Journal of nature 15(1): 39-45.

4. Komenaka IK, Ditkoff BA, Joseph KA, Russo D, Gorroochurn P, Ward M, Horowitz E, El-Tamer MB, Schnabel FR (2004) The Development of Interval Breast Malignancies in Patients with BRCA Mutations. Cancer 100(10): 2079-83.

5. Heiman GA, Hodge SE, Gorroochurn P, J Zhang, Greenberg DA (2004) Effect of population stratification on case-control association studies. I: Elevation in the false positive rates and comparisons to confounding risk ratios (a simulation study). Hum Hered 58: 30-39.(pdf)

6. Gorroochurn P, Hodge SE, Heiman GA, Greenberg DA (2004) Effect of population stratification on case-control association studies. II: False-positive rates and their limiting behavior as number of subpopulations increases. Hum Hered 58:  40-48. (pdf)

7. Heiman, GA, Gorroochurn P, Hodge SE, Greenberg DA (2005) Robustness of case-controls studies. Cancer Epidemiol Biomarkers Prev 14(6).(pdf)

8. Gorroochurn P , Hodge SE (2006) Estimating allele frequencies and inbreeding coefficients in k-allele models. Math Pop Studies, 13: 83-103.(pdf)

9. Gorroochurn P, Heiman GA, Hodge SE, Greenberg DA (2006) Centralizing the non-central chi-square: A new method to correct for population stratification in genetic case-control association studies. Genet Epidemiol, 30: 277-289.(pdf)

10. Bemis DL, Capodice JL, Gorroochurn P, Katz AE, and Buttyan R (2006) Anti-prostate cancer activity of a beta-carboline alkaloid enriched extract from Rauwolfia vomitoria. Int. J Oncol. 29 (5):1065-1073.

11. Durner M, Gorroochurn P, Marini C, and Guerrini R (2006) Editorial Commentary: Can We Increase the Likelihood of Success for Future Association Studies in Epilepsy? Epilepsia 47 (10):1617-1621.(pdf)

12. Fine R L, Shah S S, Moulton TA, Yu IR, Fogelman DR, Richardson M, Burris HA, Samuels BL, Assanasen C, Gorroochurn P, Hibshoosh H, Orjuela M, Garvin J, Goldman FD, Dubovsky D, Walterhouse D, Halligan G (2007) Androgen and c-Kit receptors in desmoplastic small round cell tumors resistant to chemotherapy: novel targets for therapy. Cancer Chemother. Pharmacol. 59 (4):429-437.

13. Gorroochurn P, Hodge SE, Heiman GA and Greenberg DA (2007) Invited Article: A unified approach for quantifying, testing and correcting population stratification in case-control association studies. Hum Hered 64: 149-159.(pdf)

14. Gorroochurn P, Hodge SE, Heiman GA, Durner M, Greenberg DA (2007). Commentary: Non-replication in association studies: 'pseudo-failures' to replicate? Genetics in Medicine 9(6): 325-331.(pdf)

15. Heiman GA, Ogburn E, Gorroochurn P, Keyes KM, and Hasin D (2008) Evidence for a two-stage model of dependence using the NESARC and its implications for genetic association studies. Drug Alcohol Depend. 92 (1-3):258-266.

16. Zweben A, Pettinati HM, Weiss RD,Youngblood M, Cox CE, Mattson ME, Gorroochurn P, Ciraulo D. (2008) Relationship between Medication Adherence and Treatment Outcomes: THE COMBINE STUDY. Alcoholism: Clinical and Experimental Research 32(9):1661-9.

17. Yaeger R, vila-Bront A, Abdul K, Nolan PC, Grann VR, Birchette MG, Choudhry S, Burchard EG, Beckman KB, Gorroochurn P, Ziv E, Consedine NS, Joe AK (2008) Comparing genetic ancestry and self-described race in african americans born in the United States and in Africa. Cancer Epidemiol Biomarkers Prev 17:1329-1338.


18. Gorroochurn P (2008) Perils in the Use of Linkage Disequilibrium for Fine Gene Mapping: Simple Insights from Population Genetics. Cancer Epidemiol Biomarkers Prev 17: 3292-3297.(pdf)

19. Gorroochurn P, Hodge SE, Heiman GA and Greenberg DA (2009) Comments on: Review and Evaluation of Methods Correcting for Population Stratification with a Focus on Underlying Statistical Principles Hum Hered. 67:145–146.

20. Petukhova L, Shimomura Y, Wajid M, Gorroochurn P, Hodge SE,  Christiano AM (2009) The effect of inbreeding on the distribution of compound heterozygotes: a lesson from lipase H mutations in autosomal recessive woolly hair. Hum Hered. 68: 117-130.

21. Capodice JL, Gorroochurn P, Cammack AS, Eric G, McKiernan JM, Benson MC, Stone BA, Katz AE (2009) Zyflamend in men with high-grade prostatic intraepithelial neoplasia: results of a phase I clinical trial. J Soc Integr Oncol. 7(2):43-51.

22. Pinto RM, Yu G, Spector AY, Gorroochurn P, McCarthy D (2010). Substance abuse treatment providers’ involvement in research is associated with willingness to use findings in practice. Journal of Substance Abuse Treatment 39: 188–194.

23. Gorroochurn P, Hodge SE, Heiman GA and Greenberg DA (2010). Comments on ‘Delta-Centralization Fails to Control for Population Stratification in Genetic Association Studies. Hum Hered. 69:295.

24. Wright JD, St. Clair CM, Deutsch I, Burke WM, Gorroochurn P; Sun X, Herzog TJ (2010) Pelvic Radiotherapy and the Risk of Secondary Leukemia and Multiple Myeloma. Cancer 116(10): 2486-2492.

25. Alam ML, Van der Schueren BJ, Ahren B, Wang GC, Swerdlow NJ, Arias S, Bose M, Gorroochurn P, Teixeira J, McGinty J, Laferrère B (2011) Gastric bypass surgery, but not caloric restriction, decreases dipeptidyl peptidase-4 activity in obese patients with type 2 diabetes. Diabetes Obes Metab.13(4): 378-381.


26. Drake RE, Caton C, Xie H, Hsu E, Gorroochurn P, Samet S, Hasin D (2011). A Prospective 2-year Study of Emergency Department Patients with Early-phase Primary Psychoses or Substance-induced Psychoses. The American Journal of Psychiatry. 168(2): 742-748.

27. Herman D, Conover S, Gorroochurn P, Hinterland K, Hoepner L, Susser E (2011) A Randomized Trial of Critical Time Intervention to Prevent Homelessness in Persons with Severe Mental Illness following Institutional Discharge. Psychiatr Serv. 62(7):713-9.

28. Pinto RM, Campbell ANC, Hien D, Yu G, Gorroochurn P (2011). Retention in the NIDA Clinical Trials Network Women and Trauma Study: Implications for Post-trial Implementation. American Journal of Orthopsychiatry. 81(2): 210-216.

29. Gorroochurn P, Hodge SE, Heiman GA, Greenberg DA (2011). An Improved Delta-Centralization Method for Population Stratification. Human Heredity. 71(3): 180-185.(pdf)

30. Gorroochurn, P (2011) Use the Correlation Coefficient to Summarize Regression Performance?" Teaching Statistics. 33: 81-82.

31. Laferrère B, Reilly D, Arias S, Swerdlow N, Gorroochurn P, Bose M, Bawa B, Tiexeira J, Stevens RD ,Wenner BR, Bain JR, et al. (2011). Differential Metabolic Impact of Gastric Bypass Surgery Versus Dietary Intervention in Obese Diabetic Subjects Despite Identical Weight Loss. Sci. Transl. Med. 3(80), 80re2.

32. Van der Schueren B, Green N, Gorroochurn P, Teixeira J, Altiner S, Laferrère B (2011) Low Vitamin D in Candidates for Bariatric Surgery: Are the Americans Better Off than the French? Obesity Surgery. 21(7): 948-949.

33. Gorroochurn P (2011). Errors of Probability in Historical Context. American Statistician. 65(4): 246-254. (Also in ‘The Best Writings on Mathematics 2013,’ edited by M. Pitici, Princeton University Press 2014)(pdf)

34. Shah SH, Crosslin DR, Haynes CS, Nelson S, Turer CB, Stevens RD, Muehlbauer MJ, Wenner BR, Bain JR, Laferrère B, Gorroochurn P, Teixeira J, Brantley PJ, Stevens VJ, Hollis JF, Appel LJ, Lien LF, Batch B, Newgard CB, Svetkey LP. (2012). Branched-chain amino acid levels are associated with improvement in insulin resistance with weight loss. Diabetologia. 55(2):321-30.

35. Gorroochurn, P (2012) Some Laws and Problems of Classical Probability and How Cardano Anticipated Them. Chance 25.4: 13-20.(pdf)

36. Smolak A, Gorroochurn P, Kamarulzaman A, Janjua N (2012) Asian public concern over the ethics of scientists: Predictors and implications for research ethics. Accountability in Research 19: 370-382.

37. Edge MD, Gorroochurn P, Rosenberg NA (2013) Windfalls and pitfalls: Applications of population genetics to the search for disease genes (2013) Evolution, Medicine, and Public Health 2013 (1): 254-272. (pdf)

38. Gorroochurn P, Levin B (2013) On Two Historical Aspects of Buffon's Needle Problem. Electronic Journal for History of Probability and Statistics 9, pp. 40. (pdf)

39. McQuistion HL, Gorroochurn P, Hsu E, Caton CLM (2014) Risk Factors Associated with Recurrent Homelessness After a First Homeless Episode. Community Mental Health Journal 50 (5): 505-513.

40. Yin B, Levy D, Meadows M, Moen T, Gorroochurn P, Cadet ER, Levine WN, Ahmad CS (2014) How Does External Rotation Bracing Influence Motion and Functional Scores After Arthroscopic Shoulder Stabilization? Clinical Orthopaedics and Related Research 472(8): 2389-96.

 41. Gorroochurn P (2014) Thirteen Correct Solutions to the "Problem of Points" and their Histories. The Mathematical Intelligencer 36(3): 56-64. (pdf)

42. Burnes D., Rizzo V.M., Gorroochurn P., Pollack M., & Lachs M.S. (2014). Understanding Service Utilization in Cases of Elder Abuse to Inform Best Practices. Journal of Applied Gerontology 35(10): 1036-1057.

43. Makhni E.C., Lee R.W., Morrow Z.S., Gualtieri A.P., Gorroochurn P., Ahmad C.S. (2015) Performance, Return to Competition, and Reinjury After Tommy John Surgery in Major League Baseball Pitchers: A Review of 147 Cases. The American Journal of Sports Medicine 42(6): 1323-1332.

44. Cadet E.R., Babatunde O.M., Gorroochurn P., Chan A. K., Stancato A., Brown M., Johnson S., Kaiser P.B., Gardner T., Ayeni O.R. (2016) Inter and intraobserver agreement of femoroacetabular impingement (FAI) parameters comparing plain radiographs and advanced, 3D computed tomographic (CT)generated hip models in a surgical patient cohort. Knee Surg Sports Traumatol Arthrosc: 24(7): 2324-31.

45. Chen F.-P., Samet S., Gorroochurn P., O’Hara K.M. (2016) Characterizing Factors of Employment Status in Persons with Major Depressive Disorder. Evaluation & the Health Profession 39: 263-281.

46. Gorroochurn P. (2016) On Galton’s Change from ‘Reversion’ to ‘Regression’. American Statistician 70(3): 227-231.(pdf)

47. Bobman J.T., Danoff J.R., Babatunde O.M., Zhu K., Peyser K., Geller J.F., Gorroochurn P., Macaulay W. (2016) Total Hip Arthroplasty Functional Outcomes are Independent of Acetabular Component Orientation when a Polyethylene Liner is Employed. The Journal of Arthroplasty 31(4): 830-834.

48. Danoff J.R., Bobman J.T., Cunn G., Murtaugh T., Gorroochurn P., Geller J.F., Macaulay W. (2016)  Redefining the Acetabular Component Safe Zone for Posterior Approach Total Hip Arthroplasty. The Journal of Arthroplasty 31(2): 506-511

49. Schinke S., Schwinn Y., Hopkins J., Gorroochurn P., Wahlstrom L. (2017) Is the Legalization of Marijuana Associated With Its Use by Adolescents? Substance Use & Misuse 52(2):256-258.

50. Blackburn C.W., Vossoughi S.R., Ojo B., Gorroochurn P., Marboe C.C., Akelina Y., Strauch R.J. (2017) Comparison of the Minimal-Touch Technique and the Eversion Technique for Microvascular Anastomosis in a Rat Model. J Reconstr Microsurg 33(2): 97-102.

51. Gorroochurn P. (2017) God Does Not Play Dice: Revisiting Einstein’s Rejection of Probability in Quantum Mechanics.  Math. Scientist 42: 61-73.(pdf)

52. Conway A., Modrek, A., Gorroochurn P. (2018) Maternal Sensitivity Predicts Fewer Sleep Problems at Early Adolescence for Toddlers with Negative Emotionality: A Case of Differential Susceptibility. Child Psychiatry Hum Dev 49(1): 86-99.

53. Makhni M.C., Jegede K., Lombardi J., Whittier S., Gorroochurn P., Lehman R.A., Riew KD (2018) No Clear Benefit of Chlorhexidine Use at Home Before Surgical Preparation. J Am Acad Orthop Surg. 26 (2): e39-e47

54. Gates L.B., Pearlmutter S., Keenan K., Divver C., Gorroochurn P. (2018) Career Readiness Programming for Youth in Foster Care. Children and Youth Services Review 89: 152-164

55. Gorroochurn P. (2018) The End of Statistical Independence: The Story of Bose-Einstein Statistics. The Mathematical Intelligencer 40 (3): 12-17.

56. Mascayano F., Alvarado R., Andrews H.F., Jorquera M.J., Lovisi G.M., de Souza F.M., Pratt C., Rojas G., Restrepo-Toro M.E, Fader K., Gorroochurn P., Galea S., Dahl C.M., Cintra J., Conover S., Burrone M.S., Baumgartner J.N., Rosenheck R., Schilling S., Sarução K.R., Stastny P., Tapia E., Cavalcanti M.T., Valencia E., Yang L.H., Susser E. (2019) Implementing the protocol of a pilot randomized controlled trial for the recovery-oriented intervention to people with psychoses in two Latin American cities. Cadernos de Saúde Pública: 35(4): 1-10

57. Poon S., Nellans K., Rothman A., Crabb R.A.L, Wendolowski S.F., Kiridly D., Gecelter R., Gorroochurn P., Chahine N.O. Underrepresented Minority Applicants Are Competitive for Orthopaedic Surgery Residency Programs, but Enter Residency at Lower Rates (2019). Journal of the American Academy of Orthopaedic Surgeons 27(21): e957-e968.

58. Griffith T., Ahmad C.S., Gorroochurn P., D’Angelo J., Ciccotti M.G., Dines J., Alchek D.W., Camp C.L. (2019) Comparison of Outcomes Based on Graft Type and Tunnel Configuration for Primary Ulnar Collateral Ligament Reconstruction in Professional Baseball Pitchers. The American Journal of Sports Medicine 47(5): 1103-1110

59. Gorroochurn P. (2019) Probability and Kinetic Theory: A Tale of Two Disciplines. The Mathematical Intelligencer 41(2): 42-56.

60. Crowley S.G., David P. Trofa D.P., Vosseller J.T., Gorroochurn P., Redler L.H., Schiu B., Popkin C.A. Epidemiology of Foot and Ankle Injuries in National Collegiate Athletic Association Men’s and Women’s Ice Hockey. Orthopaedic Journal of Sports Medicine (in press)

61. de Paula T.R., Gorroochurn P., Kiran, R.P., Keller D.S. (2019) Does Adjuvant Chemotherapy Improve Survival in T3N0 Rectal Cancer? An Evaluation of Use and Outcomes from the National Cancer Database (NCDB). Journal of Gastrointestinal Surgery (in press)

62. Gorroochurn P. (2020) Who Invented the Delta Method, Really? The Mathematical Intelligencer (in press)






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