Mathematics Problem of the Week

Fall 2004

POW 8: Flippin’ Out!

It’s very easy to use a fair coin to decide between two alternatives - just assign Heads (H) to one and Tails (T) to the other and a flip gives each a ½ chance of either alternative being chosen.

If we had four alternatives, say A, B, C and D we could flip two coins with A=HH, B=TH, C=HT and D=TT giving ¼ probability of choosing each alternative.

Can we devise a scheme to use one or more fair two-sided coins (including repeated flips) to decide among three alternatives (i.e. get a probability of 1/3) or among five alternatives (1/5)?

If not, explain why not.

If so, describe the scheme(s) in detail and justify that the required probability is obtained.

Due Friday, October 29^th at Noon.

Solutions should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/