exercise:301ad4198d: Difference between revisions
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(Created page with "<div class="d-none"><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></div> 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 h...") |
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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 | |||
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 | <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 | side being searched, each member will find the boy with probability | ||
Latest revision as of 23:10, 12 June 2024
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]?