Legal Statistics and Probabilities Quiz

Understanding Probabilities and Bayes' Theorem

• Likelihood Ratio (LR) is used in DNA evidence to determine the probability of finding a match from a particular population.
• Bayes' theorem provides a rule for updating probabilities about a proposition in the light of new evidence.
• Bayes' theorem and LR are used to calculate the posterior odds for a proposition in the context of a screening test for doping in sports.
• In a hypothetical example, a screening test for doping claiming to be ‘95% accurate’ results in a posterior probability of doping of approximately 28%.
• Bayes' theorem is crucial in interpreting test results and can prevent misinterpretations of test accuracy, as seen in the example of doping screening.
• Mammograms are used as a screening tool for breast cancer, and Bayes' theorem can be applied to understand their accuracy.
• Given the prevalence of breast cancer (1%) and the sensitivity (80%) and specificity (90%) of mammograms, Bayes' theorem can be used to calculate the probability of actually having breast cancer given a positive mammogram result.
• The probability of having cancer given a positive test result is calculated using the sensitivity, prevalence of breast cancer, and overall probability of a positive test result.
• Human intuition often struggles with assessing how 'surprising' an event truly is, especially when it comes to rare events and coincidences.
• The perception of an event being surprising for an individual may not align with the reality of its probability when considering a larger group.
• The concept of coincidences is illustrated with the example of three major plane crashes occurring within an eight-day period in 2014, which has approximately a 60% probability over a ten-year span.
• Understanding probabilities and applying Bayes' theorem is essential for interpreting test results accurately and avoiding misinterpretations of the likelihood of certain events.

Understanding Statistical Science and Probabilities in Legal Proceedings

• Statistical science supports expert knowledge in evaluating various types of evidence in legal proceedings, including DNA evidence, trace evidence, and pattern-matching evidence.
• Transparency in data and reasoning is crucial when drawing conclusions based on statistical science in legal proceedings, following the concept of "intelligent transparency."
• Probabilities of all possible events add up to 1, and they are multiplied for independent events and added for mutually exclusive events.
• Probability is presented as a subjective measure, dependent on the observer's knowledge and assumptions, and it changes with new information.
• In legal contexts, probability is used to make informed judgments based on available data and should be grounded in empirical evidence.
• Personal probabilities, also known as personal ‘degrees of belief,’ are made based on individuals' knowledge and understanding of the factors and risks involved.
• Experts assign personal probabilities based on their experience, knowledge, and understanding, but the reliability of expert-assigned probabilities is influenced by various factors.
• The probative value in legal proceedings is expressed as a likelihood ratio (LR), which is the probability of the evidence assuming that one proposition is true divided by the probability assuming another proposition is true.
• Likelihood ratios are often used in DNA evidence to express the probability that the suspect's DNA matches the DNA trace found at the crime scene, compared to the probability that it originates from someone else.