Python Programming for Biology: Bioinformatics and Beyond

Figure 21.1.  Sample space size for sequential events. The calculations to give the size

of the sample space are shown for three subsequent rolls of a die and three positions in a

DNA sequence. The sample space represents the totality of all possible outcomes. For a

sequence of events, where each has a fixed number of possibilities, the size of the sample

space is the product of the numbers of possibilities at each point in the sequence.

Probability values

Probabilities  are  values  between  zero  and  one  (between  impossibility  and  certainty)  that

we assign to the outcomes of a random process. The summation of all probabilities, over

all  possible  outcomes,  is  exactly  one.  In  effect,  each  outcome  occupies  a  fraction  of

likelihood from the certainty that something happens in a random process. Hence for a roll

of an unbiased die the probability assigned to each of the six possible outcomes is

1

/

6

, so

they  all  add  up  to  one.  As  illustrated  in

Figure  21.2

,  this  can  be  visualised  by  each

outcome  taking  a  different  fraction  of  a  line  of  unit  length,  though  the  order  of  the

resulting  regions  is  unimportant.  Note  that  we  introduce  the  notation  Pr(X),  which  is

shorthand to mean the probability of X occurring, whatever occurrence X may be.

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