Classical and Legal Probability
Probability in mathematical statistics is classically defined in terms of the outcomes of conceptual experiments, such as tossing ideal coins and throwing ideal dice. In such experiments the probability of an event, such as tossing heads with a coin, is defined as its relative frequency in long-run trials. Since the long-run relative frequency of heads in tosses of a fair coin “closes in” on one-half, we say that the probability of heads on a single toss is one-half. Or, to take a more complicated example, if we tossed a coin 50 times and repeated the series many times, we would tend to see 30 or more heads in 50 tosses only about 10% of the time; so we say that the probability of such a result is one-tenth. We refer to this relative frequency interpretation as classical probability. Calculations of classical probability generally are made assuming the underlying conditions by which the experiment is conducted, in the above examples with a fair coin and fair tosses.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
J. Bernoulli, Ars Conjectandi [The Art of Conjecturing] 225 (1713), quoted in S.M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900 at 65 (1986).
- 2.
214 N.Y. 75 (1915).
- 3.
Id. at 85.
- 4.
To be sure, the court’s rejection of the testimony was correct because there were other, valid objections to it. See p. 49.
- 5.
State v. Kim, 398 N.W. 2d 544 (1987); State v. Boyd, 331 N.W. 2d 480 (1983).
- 6.
State v. Boyd, 331 N.W. 2d at 483.
- 7.
The Minnesota Supreme Court’s opinions seem unduly restrictive of valuable evidence and its rulings were overturned by statute with respect to genetic or blood test results. The statute provides: “In a civil or criminal trial or hearing, statistical population frequency evidence, based on genetic or blood test results, is admissible to demonstrate the fraction of the population that would have the same combination of genetic markers as was found in a specific human biological specimen. ‘Genetic marker’ means the various blood types or DNA types that an individual may possess.” Minn. Stat. Sec. 634.26 (2008).
- 8.
D.L. Faigan & A.J. Baglioni, Jr., Bayes’ Theorem in the Trial Process, 12 Law and Human Relations 1 (1988).
- 9.
The chestnut is from Smith v. Rapid Transit, Inc., 307 Mass. 469 (1945). The doctoring is from D. Kahneman, A. Tversky & P. Slovic (eds.), Judgment Under Uncertainty: Heuristics and Biases 1 (1982).
- 10.
The odds on an event are defined as the probability that the event will occur, p, divided by the probability that it will not, 1 − p. Conversely, the probability of an event is equal to the odds on the event divided by one plus the odds.
- 11.
Empirical studies based on simulated trials show a similar underweighting. See, e.g., J. Goodman, “Jurors’ Comprehension and Assessment of Probabilistic Evidence”, 16 American Journal of Trial Advocacy 361 (1992).
- 12.
See, e.g., Judgment Under Uncertainty: Heuristics and Biases at 4–5 (D. Kahneman, P. Slovic, and A. Tversky, eds., 1982).
- 13.
Cf. United States v. Lopez, 328 F. Supp. 1077 (E.D.N.Y. 1971).
- 14.
For a discussion of the Supreme Court cases, see M.O. Finkelstein & B. Levin, “On the Probative Value of Evidence from a Screening Search,” 43 Jurimetrics Journal 265, 270–276 (2003).
- 15.
523 U.S. 303 (1998).
- 16.
These results are not much changed if it is assumed that none of the pending cases resulted in adverse action against individuals. In that scenario, the likelihood ratio is between 1.95 and 6.8, respectively.
- 17.
The definition of “relevant evidence” in the Federal Rules of Evidence is “evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.” FED. R. EVID. 401. A polygraph test with an LR of about 2 is certainly relevant evidence by that definition.
- 18.
Scheffer, 523 U.S. at 312–17. Justice Thomas gave as additional reasons for sustaining Rule 707 that the exclusion of polygraph evidence preserved the court members’ core function of making credibility determinations, avoided litigation over collateral issues, and did not preclude the defense from introducing any factual evidence, as opposed to expert opinion testimony.
- 19.
Whether people conform their personal probabilities to the assumptions has also been questioned.
- 20.
Taken from M.O. Finkelstein & W. Fairley, “A Bayesian Approach to Identification Evidence,” 83 Harvard Law Review 489 (1970).
- 21.
For such a person the prior odds are 0.25/0.75 = 1/3. The likelihood ratio is 1 (we are certain that the palm print would be like the defendant’s if he left it) divided by 1/1,000 (the rate of such palm prints in the population if he didn’t leave it), or 1,000. Applying Bayes’s theorem, 1/3 × 1,000 = 333.33 (the posterior odds). The posterior probability of guilt is thus 333.33/334.33 = 0.997.
- 22.
Regina v. Alan James Doheny and Gary Adams, [1996] EWCA Crim. 728 (July 31, 1996).
- 23.
96 Me. 207 (1902).
- 24.
Id. at 217–218.
- 25.
307 Mass. 246 (1940).
- 26.
307 Mass. at 250 (citations omitted).
- 27.
See, e.g., Guenther v. Armstrong Rubber Co., 406 F.2d 1315 (3rd Cir. 1969) (holding that although 75–80% of tires marketed by Sears were made by defendant manufacturer, plaintiff would have lost on a directed verdict even if he had been injured by a tire bought at Sears).
- 28.
Howard v. Wal-Mart Stores, Inc., 160 F. 3d 358, 359--60 (7th Ci. 1998) (Posner, C.J.).
- 29.
402 F. 3d 489 (5th Cir. 2005).
- 30.
Commonwealth v. Clark, 292 Mass. 409, 415 (1935) (Lummus, J.) (citations omitted).
- 31.
In re Agent Orange Product Liability Lit., 611 F. Supp. 1223, 1231–1234 (E.D.N.Y 1985), aff ’d, 818 F.2d 187 (2d Cir. 1987) (Agent Orange used in Vietnam and various ailments); Daubert v. Merrell Dow Pharmaceuticals, Inc., 43 F.3d 1311 (9th Cir. 1995) (Bendectin and birth defects); Hall v. Baxter Healthcare Corp., 947 F. Supp. 1387 (D. Ore. 1996) (silicone breast implants and connective tissue disease).
- 32.
Hawkins v. Jones, Doc. Nos. P-2287/86 K and P-3480/86 K (N.Y. Family Ct. Jan. 9, 1987).
- 33.
“Paternity Test at Issue in New Jersey Sex-Assault Case,” The New York Times November 28, 1999 at Bl.
- 34.
State v. Spann, 130 N.J. 484 (1993).
- 35.
Plemel v. Walter, 303 Ore. 262 (1987).
- 36.
Connecticut v. Skipper, 228 Conn. 610 (1994).
- 37.
Regina v. Dennis John Adams, EWCA Crim 222, transcript at *13 (April 26, 1996), quoted with approval in Regina v. Alan Doheny & Gary Adams, [1996] EWCA Crim 728, transcript at *4 (July 31, 1966) (dictum).
- 38.
Committee on Scientific Assessment of Bullet Lead Elemental Composition Comparison, Forensic Analysis: Weighing Bullet Lead Evidence, 96, 97, 112 (The National Academies Press, 2004).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Finkelstein, M.O. (2009). Probability. In: Basic Concepts of Probability and Statistics in the Law. Springer, New York, NY. https://doi.org/10.1007/b105519_1
Download citation
DOI: https://doi.org/10.1007/b105519_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-87500-2
Online ISBN: 978-0-387-87501-9
eBook Packages: Humanities, Social Sciences and LawLaw and Criminology (R0)