Python Programming for Biology: Bioinformatics and Beyond

Combining probabilities

The  final  major  rule  with  probability  theory  is  about  how  we  combine  probabilities.  If

there are mutually exclusive outcomes then the probability of the event that any of these

particular  outcomes  occurs  is  the  sum  of  their  individual  probabilities.  In  mathematical

terms we describe an event formally as a set of different outcomes. Also, by saying that if

an event is defined by one outcome or another (or another etc.) then it can be described in

set  theory  terms  as  the  union  of  the  outcomes.  Taking  the  roll  of  two  fair  dice  as  an

example,  as  we  have  already  illustrated  there  are  36  possible  outcomes  each  with

probability

1

/

36

. If we want to know the probability that the total on the two dice is seven,

then  we  first  consider  which  of  the  outcomes  contribute  to  this  event  (as  illustrated  in

Figure 21.4

) and then add the probabilities for each.

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