Due November 15

This problem is best solved by doing experiments, especially with a computer, but a very clever student might be able to compute the answer. We consider this to be an hard problem, worth 20 points. Send answers and questions to mathstat@uoguelph.ca

Suppose we flip a coin 20 times and then find the largest number of either heads or tails in a row. Five examples follow with the longest run of heads or tails in parenthesis. These examples were generated by flipping a loonie.

CoinsLongest run
HHTHHTH(TTTT)HHTHHTTHH4
HTT(HHH)TTHHHTHHTHHTHH3
HH(TTTT)HTHHHTHTHTTHTT4
HTHTHTHTHT(HHHH)TTHTHH4
TTT(HHHHH)TTHHHTTHTHTH5
Your goal is to estimate what the average length of the longest run is. be sure to explain your technique in you e-mail as well as giving us the answer. Send your answer to mathstat@uoguelph.ca
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