Bayesian Statistics: An Introduction, 4th Edition

1.2 Examples on Bayes’ Theorem

1.2.1 The Biology of Twins

Twins can be either monozygotic (M) (i.e. developed from a single egg) or dizygotic (D). Monozygotic twins often look very similar and then are referred to as identical twins, but it is not always the case that one finds very striking similarities between monozygotic twins, while some dizygotic twins can show marked resemblances. Whether twins are monozygotic or dizygotic is not, therefore, a matter which can be settled simply by inspection. However, it is always the case that monozygotic twins are of the same sex, whereas dizygotic twins can be of opposite sex. Hence, assuming that the two sexes are equally probable, if the sexes of a pair of twins are denoted GG, BB or GB (note GB is indistinguishable from BG)

It follows that

from which it can be seen that

so that although it is not easy to be certain whether a particular pair are monozygotic or not, it is easy to discover the proportion of monozygotic twins in the whole population of twins simply by observing the sex distribution among all twins.

1.2.2 A political example

The following example is a simplified version of the situation just before the time of the British national ...