4.1 Two Events
So far we have only investigated a single event and its complement. We now pass to two events and the relationships between them. To fix ideas, consider these two events that you are contemplating now but that refer to what happens one year in the future:
Inflation next year will exceed 4%, and
Unemployment next year will exceed 9% of the workforce.
These are two events of economic importance about which you are uncertain, and which are to be discussed in connection with a fixed knowledge base. It is tedious to have to spell out the whole sentences describing the events each time they are mentioned, so let us simply call the first event high and the second many. The complementary event, high not happening, will be termed low, and the complement of many will be few. So you are uncertain about high (inflation above 4%) and about many (unemployed above 9%). By taking the event high on its own, you can proceed as in the previous chapter and assess the probability of high using the comparison with red and white balls in an urn. Suppose you think that if there are 40 red balls (and 60 white) in the urn, then the uncertainty of a red ball being drawn at random is the same as that of high inflation, then the probability of high inflation for you is 0.40 (and of low, 0.60).
Now let the same thing be done for the event of many unemployed, but to avoid confusion, in the new urn, also with 100 balls, replace red by spotted and white by plain. Then you ...