Are you asking if you need to determine the probability, as in "Do I really need to determine... ?"?

No, it's conditional probability.

The left-hand side should be P(A or B), but this equality is not relevant to this problem. Use the definition of conditional probability: P(A | B) = P(A and B) / P(B). In fact, this is the familiar formula for probability: the number of successful outcomes divided by the total number of outcomes. The difference is that in computing the probability of an event A provided a different event B is known to occur, the sample space (the set of outcomes) is restricted to outcomes in B. Here, instead of all customers, the new sample space consists of only those customers that bought a shirt, and the successful outcomes are those who in addition to a shirt also bought a tie.