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The Cliff-Hanger

A long day hiking through the Grand Canyon has discombobulated this tourist. Unsure of which way he is randomly stumbling, 1/3 of his steps are towards the edge of the cliff, while 2/3 of his steps are towards safety. From where he stands, one step forward will send him tumbling down. What is the probability that he can escape unharmed?

Note: After using the simulation, try using an applet that performs a hundred, thousands, or even a million runs at once and that allows you to change the probability of stepping toward the edge.




Trial #

Steps Forward
Steps Backward
Total Steps

Simulation Credits

  • Original Java Applet by Nick Exner (7/21/1998)
  • Modified by Nick Exner (3/1/2005)
  • JavaScript+HTML5 Remake by Nick Exner (10/25/2014)
  • Modified by Evan Ramos (2015)


  • Mosteller, Frederick, Fifty Challenging Problems in Probability with Solutions, New York: Dover Publications, Inc., 1965.