George Wolford has suggested the following variation on the Linda problem (see Exercise). The registrar is carrying John and Mary's registration cards and drops them in a puddle. When he pickes them up he cannot read the names but on the first card he picked up he can make out Mathematics 23 and Government 35, and on the second card he can make out only Mathematics 23. He asks you if you can help him decide which card belongs to Mary. You know that Mary likes government but does not like mathematics. You know nothing about John and assume that he is just a typical Dartmouth student. From this you estimate:

[[math]] \begin{array}{ll} P(\mbox {Mary\ takes\ Government\ 35}) &= .5\ , \\ P(\mbox {Mary\ takes\ Mathematics\ 23}) &= .1\ , \\ P(\mbox {John\ takes\ Government\ 35}) &= .3\ , \\ P(\mbox {John\ takes\ Mathematics\ 23}) &= .2\ . \end{array} [[/math]]

Assume that their choices for courses are independent events. Show that the card with Mathematics 23 and Government 35 showing is more likely to be Mary's than John's. The conjunction fallacy referred to in the Linda problem would be to assume that the event “Mary takes Mathematics 23 and Government 35” is more likely than the event “Mary takes Mathematics 23.” Why are we not making this fallacy here?