Statistics and the Evaluation of Evidence for Forensic Scientists - Franco Taroni

Скачать книгу

images images images

      This law may be generalised to more than two events. Consider images events images. If they are mutually independent then

equation

      

      1.7.10 Law of Total Probability

      (1.11)equation

      a generalisation of the second law of probability, (1.7), for exclusive events. Consider as an example allelic distributions at a locus, e.g. locus TPOX. There are five alleles, images, and 12, and these are mutually exclusive and exhaustive.

      Consider images for events images and images. Let images be any other event. The events ‘images and images’ and ‘images and images’ are exclusive. They cannot both occur. The event “‘images and images’ or ‘images and images’ ” is simply images. For example, let images be male, images be female, images be left‐handed. Then

       ‘’ denotes a left‐handed male,

       ‘’ denotes a left‐handed female.

      The event ‘ “images and images” or “images and images” ’ is the event that a person is a left‐handed male or a left‐handed female, which implies the person is left‐handed (images). Thus,

equation

       Law of Total Probability

      If images are images mutually exclusive and exhaustive events,

      (1.12)equation

      This is sometimes known as the extension of the conversation (Lindley 1991)

      An example for blood types and paternity cases is given by Lindley (1991). Consider two possible groups, images (Rhimages) and images (Rh+) for the father, so here images. Assume the relative frequencies of the two groups are images and images, respectively. The child is Rhimages (event images) and the mother is also Rhimages (event images). The probability of interest is the probability a Rhimages mother will have a Rhimages child, in symbols images. This probability is not easily derived directly but the derivation is fairly straightforward if the law of total probability is invoked to include the father.