There is a relationship between the *s P(AB) and P(A I B). It is called the multiplication rule for probabilities:
P(AB) = P(A I B) * P(B)
In words this is: "the probability of A and B is the probability of A given B times the unconditional probability of B."
We can manipulate this to give the following representation for a conditional probability: P (A I B) = P(AB) / P(B)
Example:We will assume the probabilities in the list below:

  1. The probability of the monetary authority increasing interest rates "I" is 40%: P(I) = .4

  2. The probability of a recession "R" given an increase in interest rates is 70%: P(R given I) = .7

  3. The probability of "R" without an increase in interest rates is 10%: P(R given IC) = .1

Without additional information, we can assume that the events "increase in interest rates" and "no increase in interest rates" are the only possible events. They are mutually exclusive and exhaustive, and since there are only two events, they are called complements. The superscript "C" stands for complement.