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    IBEasyProbability7–9

    Finding the Overlap from the Two Totals

    Descobrir a Interseção a Partir dos Dois Totais

    In a group of 40 tourists, 27 have visited Lisbon and 19 have visited Porto. Every tourist has visited at least one of the two cities. How many have visited both cities, and how many have visited exactly one of them?

    Since nobody is outside both circles, the union is the whole group. Adding the two city totals counts the people in the overlap twice, and comparing that sum with the size of the group is what reveals the overlap. Remember that "exactly one" excludes the overlap.

    Solution

    Step 1 of 8

    1. 1.Let L be the tourists who visited Lisbon and P those who visited Porto. Everybody visited at least one city, so |L \cup P| = 40.