Yael Eisenberg (Cornell University), the Eagle Problem Solvers of Georgia Southern, Chris Bistryski (PMP), and Randy Schwartz (Schoolcraft College) wrote in about this one. The condition that you were neither first nor last means that you had exactly two neighbors in line. Since presumably the order of the line was random, choosing your two neighbors is simply a way of choosing two of the other 29 people at random. There are 29 choose 2, or , ways of doing this. Nineteen of those people were COVID-free, so there are 19 choose 2, or 171 ways to choose COVID-free people. That means in the remaining cases, at least one of the neighbors has COVID. Therefore, the chance of this brush with the virus happening is %.
D. S_D19
Contributed by Christopher Bistryski, Yael Eisenberg, and Randy Schwartz, Monroe, WA, Cornell University, and Schoolcraft CollegeThis problem originally appeared in the Prisoner’s Dilemma in the issue of the PMP Newsletter. Solutions will be accepted through .