Two hundred commuters were classified by how they travel and by whether they hold a monthly pass. Metro: with pass 84, without pass 36. Bus: with pass 26, without pass 54. One commuter is picked at random from those who hold a monthly pass. What is the probability that this commuter travels by bus?

The words 'from those who hold a monthly pass' shrink the group to the pass column: 84 + 26 = 110 commuters, of whom 26 travel by bus, so the probability is 26/110 = 13/55. Dividing by all 200 surveyed gives 26/200 = 13/100 and throws the given information away. Dividing by the 80 bus riders gives 26/80 = 13/40, which conditions on the wrong line of the table — that is the probability that a bus rider holds a pass, the reverse question. The remaining 42/55 of the pass-holders travel by metro.