Principle of Probability and its Relevance in Criminal Investigation

This article sheds light on the controversial aspect of Principle of Probability and its explicit use in criminal proceedings to assess the significance of various type of evidence. “Mens rea” is one of the most important factors to prove under criminal law and for that pre assuming what was in the mind of the criminal or what he was trying to execute is one of the most ideal task. During the trial the primary task in front of the prosecution is to gather evidence and to collect these, there must be assumptions which help to finally get access to the evidence, so these assumptions are based on the principle of probability. Also, it is prerequisite in criminal cases to prove case beyond reasonable doubt so it further enhances the use of Principle of Probability.

 Probability holds a very important role when it comes to convince the jury on specific point as more the probability of the assumption more will be chances for the jury to get convinced.

In this article the application of probability in courts is explained and also the relation between critical thinking, logical reasoning and assumptions has been made. Also, the admissibility of probability evidence is explained that in what scenario the principle of probability can be used and till how far one can make assumptions and which assumptions are acknowledged by court and which not, so complete information is provided on this keeping in mind the case of State v Nicholas. [1]


Mathematically probability is a subject which concerns itself with the possible outcomes or what are the chances of a specific event to happen or how likely an event can take place in normal course of action but legally, principle of probability has a different application as principle of probability is of utmost importance during criminal investigation and is used to assess the significance of various types of evidence.

Etymologically the term probability derives from the Latin “probabilitas”, which can also mean “probity,” a measure of a witness’s legitimacy in a European legal case, and also associated with the dignity of the witness.

The concept of probability particularly deals with forensic application of probabilistic inference and probabilistic reasoning. To the top, probability is simply one aspect of logical reasoning, a little specialized where certain assumptions are made in order to reach a conclusion. During criminal investigations there is not a clear mathematical formula or way to reach to the conclusions but a set of ways or directions which an investigator needs to find or connect the dots we must say to reach a desirable conclusion. To accuse someone “beyond reasonable doubt” it becomes quintessential to have strong evidences and for the sake of that one has to make few assumptions to reach certain conclusions, the possibility of these assumptions to be true is specifically know as principle of probability in legal terms.

So, the concept of probability is quite uncertain and logical, therefore in broader sense labeled under the topic of “reasoning under uncertainty”.

Likelihood assessments are based on two factors: event “E”, whose likelihood is considered and the information “I” available to the assessor when probability of “E” is likely considered. The consequence of such an assessment is the likelihood that “E” is present, provided that “I” is known. All probabilities are based upon precise details. The event “E” can be a controversial case in the past (e.g., whether Crippen killed his wife; whether Shakespeare wrote all the plays which were credited to him conventionally?) or any future Eventuality (e.g., this ticket will National Lottery or not; that some individuals will Die young or commit a criminal offence?).

Application of Principle of Probability during Criminal Trial

During the trials the jury is just a bunch of people or observers to be precise who critically look the case and conversations among the lawyers. Their perspective towards the defendant that whether the defendant is guilty or not is totally based on evidence. For example during a murder trial the jury received an evidence that the defendant was seen near the crime scene few minutes before when the actual murder took place, so this will increase the chance for the jury to believe that the defendant is actually guilty, but then suddenly in counter to this an evidence appears justifying what the defendant was actually doing near that place and if seemed legitimate then it will make the Court think that he is not guilty. So there is lot of turbulence and ruckus during the process of trial until the exact conclusion can be made.

So, a legitimate question at this stage arises that whether there is any particular branch of knowledge or any particular normative theory that deals with the situation where uncertainty is the flagship element of the process. The answer is “yes”, probability theory is just the same. The probability of happening of an event is measured between numbers “0” to “1”. 0 depicts the least chances of happening of the event and 1 depicts the most chances. As the situation reaches the extreme ends the chances of happening and non-happening of an event becomes clear and that is the situation a court wants, to prove beyond reasonable doubt.

The principle focus of the jury is to acknowledge the legally admissible evidences by means of probability and rate the guilt of the defendant on the scale of 0-1 and then come to the conclusion of guilty or not guilty.

Admissibility of Probability Evidence in Criminal Trials

The value of evidence based on presumptions in the courts can be explained with the help of the case of State v. Nicholas[2]. Nicholas was convicted of burglary and rape. A man entered into the victim’s bedroom and raped her. Police investigation took place but no one was suspected and even the victim could not see the face of the criminal. Six months later the facts were repeated and the victim was again raped in same circumstances. In neither case’s she could see the face of the rapist but she was sure of the fact that both the times it was the same person. In the second scenario the police made a dog to follow the smell of the scent in the nearby area which lead them to Nicholas, near a school playground. His clothes matched according to the description given by the victim and police also claimed that he was sweating badly and also had an erection. A vaginal smear from the victim revealed type-o secretion. But the victim was herself type-o secretor. So the rapist had to be another type-o or a non-secretor. According to tests Nicholas was type-A (non-secretor). Thus, the test findings were incriminating.

So to give weight to this evidence or hasten the value of this evidence it is important to know that how likely or what is the probability of a person to be a non-secretor or a type-o secretor, because if these characteristics would be present very commonly than serological evidence would be of no use. Or at the other end if the probability of person being a non-secretor or a type-o secretor is very less that the case against Nicholas would be stronger. So, we can conclude that the validity of evidence especially forensic evidence is based upon the probability of the outcome which is possible and is the probability more towards “1” or “0”?

Case Laws in which Principle of Probability played a crucial role

In, Pringle v R[3] illustrates a number of difficulties with the probabilistic analysis of DNA data, including unwarranted expectations of independence; “fallacy of the prosecution” (illegitimate transposition of the conditional) at trial; obvious misunderstanding of statistical frequencies in the appeal.

In, R v Adams[4] Juries use common sense logic to reach their verdicts in criminal trials and expert witnesses should not be allowed to use mathematical methods such as Bayes ‘ Theorem to improve their ordinary logic processes – or more likely to be misled.

In, R v Dallagher [2003][5] .Expert was allowed to testify that D was very likely to be the source of an ear print at the crime scene, on the clear presumption that ear prints are exceptional in their identification 114 (despite the lack of a research base which supports this assumption). Attach, if the likelihood of an innocent match is zero there is no source likelihood error; but it is difficult to see how this statement will ever be true in the real world.

In, R  v  George  (Barry)  [2007][6] Application to scientific evidence of the basic principles of relevance and probative value The court heard testimony that if Mr. George was or was not the person who had shot the victim, Jill Dando, the research results would equally likely be received. If, as other evidence indicates, it was just as likely that a single particle of firearms discharge residue (FDR) came from some outside source as it came from a gun fired by the defendant, it was dishonest to inform the jury that innocent contamination was “highly impossible” (with the obvious implication that the FDR evidence would therefore be significantly incriminating).


Statistical evidence and probabilistic thinking impose analytical demands, including attorneys, judges, and expert witnesses, on most competent participants in criminal proceedings. There is no space for complacency; mistakes and misunderstandings about probability and statistics have led to severe judicial miscarriages. Any competent participant in criminal proceedings should preferably gain adequate knowledge of the likelihood and develop the analytical expertise required to accurately interpret statistical evidence in order to perform their respective positions in criminal justice administration. One advanced dimension of rational reasoning is probability. Criminal justice practitioners may or may not find it enlightening or useful to use the systematic methods of probability and statistics in their own clinical practice, but when used or indirectly rely on by others, they must be able to understand these techniques and effectively interpret them. In addition , the possibility of tacit or unintentional dependence on probabilistic reasoning places an even greater prime on vigilance. In short, judges, attorneys and expert witnesses should be responsible manufacturers and discerning users of statistical evidence and probabilistic reasoning once brought into criminal proceedings.

Frequently Asked Questions

  1. What is principle of probability?
  2. Significance of probability in courts or during trials?
  3. Admissibility of probability in courts?
  4. Till how far an investigator can assume during criminal investigations?
  5. Case laws where Principle of Probability played a major role.

[1] 663 P.2d 1356 (1983)

[2] 663 P.2d 1356 (1983)

[3] Appeal No. 17 of 2002, PC(Jam)

[4] (No 2) [1998] 1 Cr App R 377, CA

[5] 1 Cr App R 12, [2002] EWCA Crim 1903

[6] EWCA  Crim  2722

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