Читать книгу Statistics and the Evaluation of Evidence for Forensic Scientists - Franco Taroni - Страница 40

If two events and are such that, given background information ,

they are said to be independent. Uncertainty about is independent of the knowledge of . From (1.9) it can be seen that

Independent events are exchangeable. It is not necessarily the case that exchangeable events are independent. See Taroni et al. (2018) for a discussion. Also, two events which are mutually exclusive cannot be independent. As an example of independence, consider the rolling of two six‐sided fair dice, and say. The outcome of the throw of does not affect the outcome of the throw of . If lands 6 uppermost, this result does not alter the probability that will land 6 uppermost. The same argument applies if one die is rolled two or more times. Outcomes of earlier throws do not affect the outcomes of later throws. Similarly, with the drawing of two cards from a pack of 52 cards, if the first card drawn is replaced in the pack, and the pack shuffled, before the second draw, the outcomes of the two draws are independent. The probability of drawing two aces is 4/52 4/52. This can be compared with the probability 4/52 3/51 if the first card drawn was not replaced.