The concepts of probability and independence

The main mathematical concept needed in genetics is that of probability. When we speak of the ‘probability’ of an event, we mean the frequency with which that event occurs in a long sequence of trials. Thus the probability that a six will turn up in a single throw of a six-sided die is approximately 1/6. For most dice it is not exactly 1/6, because the spots are marked with small depressions on the surface, so that the six face is lighter than the others and so finishes uppermost more often. The important points then are:

(i) The probability of an event is defined as the frequency with which it occurs in a long sequence of trials: i.e. it is the number of ‘successes’ (e.g. sixes) divided by the total number of ‘trials’ (e.g. throws). A probability is therefore a number lying between 0 (the event never happens) and 1 (the event always happens).

(ii) All statements of probability rest ultimately on empirical measurements. Thus we know that the probability of a six is 1/6, not merely because a die has six sides, but because such dice have been thrown a large number of times, and the six falls upper-most on about 1/6 of the throws.

To take a genetical example, it is approximately true that the probability that baby born in this country will be a boy is one half.