Problem of the Week


Solutions due by high noon on Friday, April 3.

Suppose we flip a coin 20 times and then find the number of runs of either heads or tails in a row. Five examples follow with each run of heads in parenthesis (and the run of tails not in parenthesis).


Sequence of Coins

Number of Runs of Heads or Tails











Find the probability of getting exactly 5 runs.  

Either a complete probabilistic proof or computer program to approximate the answer (written in your language of choice) is appropriate.

  You may access a PDF file for the POW here or at the Sakai site.

This problem is brought to you by Prof. Ivan Ramler.

Submit your solutions to Choong-Soo Lee. You may leave a hard copy in his mailbox or submit an electronic file via Sakai.  Good luck!

Subscribe to the SLU POW electronic delivery service! Simply send a blank email to Choong-Soo Lee with the words "Subscribe POW" in the subject line. You will be among the first to receive the new POW each Friday in PDF format and also have access to the POW Sakai site. You may remove your name from the mailing list at any point by sending a similar email with a subject line reading "Unsubscribe POW". The list will be used only to send messages related to the Problem of the Week.

Official Rules