But if she first orders scones, we become even more certain. In fact, we might even suggest it: “I presume you want tea with that?” Bayes’s rule simply lets us attach numbers to this reasoning process. From Table 3.1, we see that the prior probability that the customer wants tea (meaning when she walks in the door, before she orders anything) is two-thirds. But if the customer orders scones, now we have additional information about her that we didn’t have before. The updated probability that she wants tea, given that she has ordered scones, is P(T | S) = 4/5.
