Problem of the Week

WEEK NINE

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

(HH)T(HH)T(H)TTTT(HH)T(HH)TT(HH)

11

(H)TT(HHH)TT(HHH)T(HH)T(HH)T(HH)

11

(HH)TTTT(H)T(HHH)T(H)T(H)TT(H)TT

12

(H)T(H)T(H)T(H)T(H)T(HHHH)TT(H)T(HH)

15

TTT(HHHHH)TT(HHH)TT(H)T(H)T(H)

10

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!

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