[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

A small boy is lost coming down Mount Washington. The leader

of the search team estimates that there is a probability [math]p[/math] that he came down on the east side and a probability [math]1 - p[/math] that he came down on the west side. He has [math]n[/math] people in his search team who will search independently and, if the boy is on the side being searched, each member will find the boy with probability [math]u[/math]. Determine how he should divide the [math]n[/math] people into two groups to search the two sides of the mountain so that he will have the highest probability of finding the boy. How does this depend on [math]u[/math]?