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Statistics and the Evaluation of Evidence for Forensic Scientists. Franco Taroni
Читать онлайн.Название Statistics and the Evaluation of Evidence for Forensic Scientists
Год выпуска 0
isbn 9781119245414
Автор произведения Franco Taroni
Жанр Математика
Издательство John Wiley & Sons Limited
(1.5)
Consider the drawing of a card from a well‐shuffled pack of cards with
Consider the earlier example, the rolling of a single six‐sided fair die. Then the events
This rule can be easily verified in this case where
Before discussing the third law of probability for the conjunction of two events, it is necessary to introduce the ideas of dependence and independence.
1.7.9 Dependent Events and Background Information
Consider, one roll of a fair die with
The third law of probability for dependent events was first presented by Bayes (1763) (see also Barnard 1958; Pearson and Kendall 1970; Poincaré 1912). It is the general law for the conjunction of events. Before the general statement of the third law is made, some discussion of dependence is helpful.
It is useful to consider that a probability assessment depends on two things: the event
Consider a defendant in a trial who may or may not be truly guilty. Denote the event that they are truly guilty by
All probabilities should be thought of as conditional probabilities. Personal experience informs judgements made about events. For example, judgement concerning the probability of rain the following day is conditioned on personal experiences of rain following days with similar weather patterns to the current one. Similarly, judgement concerning the value of evidence or the guilt of a PoI is conditional on many factors. These include other evidence at the trial but may also include a factor to account for the perceived reliability of the evidence. There