We have to be very careful in interpreting the 'and' of natural language. Take the following two sentences:
(1) Sarah is a university professor.
(2) Sarah is a university professor and is a feminist.
Now, the temptation is to assume that the probability of (2) should be represented as (p & q); i.e., to represent 'Linda is a university professor' and 'Linda is a feminist' as distinct events considered distinctly. But in ordinary conversation this is not the implicature of (2) at all. We tend to assume, for purposes of maximizing the value of our interactions, that whatever is expicitly stated is somehow relevant to whatever else is explicitly stated; and so the proper way to represent the probability of (2) as it would often be understood in ordinary conversation is as (p/q). That is, (2) would usually be understood in ordinary conversation as meaning 'Sarah is a university professor, given that she is a feminist' (or vice versa, depending on whether the context puts emphasis on the professorship or the feminism). The difference is quite significant.
