By Department of Mathematics
Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a panel of faculty judges, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited! Send solutions to firstname.lastname@example.org or put solutions in the marked envelope in the hallway outside Glatfelter 215. This problem was posted on Friday, October 19 and solutions are due on Friday, October 26 by 5:00 p.m.
You are standing at the top of a pyramid.
There is a network of six slides from the top of the pyramid to the safety of the ground, arranged like so (the thick dark lines are the slides).
A freak storm arrives, in which each slide has a 1/2 probability (independent of all the other slides) of getting destroyed by lightning. If a slide is destroyed, you cannot slide down it. (You can never climb up a slide, whether it is destroyed or not.)
What is the probability you will be able to slide down to the ground after the storm?