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Coin tossing (Posted on 2004-06-11) Difficulty: 3 of 5
I threw a coin n times, and never got three tails in a row. I calculated the odds of this event, and found out they were just about even; 50%-50%. How many times did I throw the coin?

A second question: what were the chances of having not gotten three heads in a row either?

See The Solution Submitted by Federico Kereki    
Rating: 3.6667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(5): Markov chain solution - 2nd part | Comment 20 of 25 |
(In reply to re(4): Markov chain solution - 2nd part by Federico Kereki)

In the problem it does not state that the coin tossing would end when either TTT or HHH was achieved.  The premise was that a certain number of tosses would be made. If the coin tossing stopped with a triple then the circumstance that was 50% probable would be ending at toss n, which wouldn't be 50% at n=10.

However, assuming what you say, and that coin tossing would have stopped at either a triple-H or triple-T, or having reached 10 tosses and givenup, and that the probability of having completed same by 10 tosses is what is sought, then the 29.6% figure is still not correct.

I've rerun the exhaustive list of 1024 outcomes of 10 tosses, but now kept track of whether TTT or HHH was achieved first in those cases where both occurred so we can keep track of what would happen if we stopped there.  This is legitimate, as, to take one example, HTTT has 1/16 probability of happening, or 64/1024, so the 64 possibilities of what comes after do count for this. I've also marked with *** those instances where only HHH was achieved, and this at the last 3 tosses only.

The annotated results are as follows, and statistics appear at the bottom, followed by the result:

HHHHHHHHHH HHH 
HHHHHHHHHT HHH
HHHHHHHHTH HHH
HHHHHHHHTT HHH
HHHHHHHTHH HHH
HHHHHHHTHT HHH
HHHHHHHTTH HHH
HHHHHHHTTT HHH TTT
HHHHHHTHHH HHH
HHHHHHTHHT HHH
HHHHHHTHTH HHH
HHHHHHTHTT HHH
HHHHHHTTHH HHH
HHHHHHTTHT HHH
HHHHHHTTTH HHH TTT
HHHHHHTTTT HHH TTT
HHHHHTHHHH HHH
HHHHHTHHHT HHH
HHHHHTHHTH HHH
HHHHHTHHTT HHH
HHHHHTHTHH HHH
HHHHHTHTHT HHH
HHHHHTHTTH HHH
HHHHHTHTTT HHH TTT
HHHHHTTHHH HHH
HHHHHTTHHT HHH
HHHHHTTHTH HHH
HHHHHTTHTT HHH
HHHHHTTTHH HHH TTT
HHHHHTTTHT HHH TTT
HHHHHTTTTH HHH TTT
HHHHHTTTTT HHH TTT
HHHHTHHHHH HHH
HHHHTHHHHT HHH
HHHHTHHHTH HHH
HHHHTHHHTT HHH
HHHHTHHTHH HHH
HHHHTHHTHT HHH
HHHHTHHTTH HHH
HHHHTHHTTT HHH TTT
HHHHTHTHHH HHH
HHHHTHTHHT HHH
HHHHTHTHTH HHH
HHHHTHTHTT HHH
HHHHTHTTHH HHH
HHHHTHTTHT HHH
HHHHTHTTTH HHH TTT
HHHHTHTTTT HHH TTT
HHHHTTHHHH HHH
HHHHTTHHHT HHH
HHHHTTHHTH HHH
HHHHTTHHTT HHH
HHHHTTHTHH HHH
HHHHTTHTHT HHH
HHHHTTHTTH HHH
HHHHTTHTTT HHH TTT
HHHHTTTHHH HHH TTT
HHHHTTTHHT HHH TTT
HHHHTTTHTH HHH TTT
HHHHTTTHTT HHH TTT
HHHHTTTTHH HHH TTT
HHHHTTTTHT HHH TTT
HHHHTTTTTH HHH TTT
HHHHTTTTTT HHH TTT
HHHTHHHHHH HHH
HHHTHHHHHT HHH
HHHTHHHHTH HHH
HHHTHHHHTT HHH
HHHTHHHTHH HHH
HHHTHHHTHT HHH
HHHTHHHTTH HHH
HHHTHHHTTT HHH TTT
HHHTHHTHHH HHH
HHHTHHTHHT HHH
HHHTHHTHTH HHH
HHHTHHTHTT HHH
HHHTHHTTHH HHH
HHHTHHTTHT HHH
HHHTHHTTTH HHH TTT
HHHTHHTTTT HHH TTT
HHHTHTHHHH HHH
HHHTHTHHHT HHH
HHHTHTHHTH HHH
HHHTHTHHTT HHH
HHHTHTHTHH HHH
HHHTHTHTHT HHH
HHHTHTHTTH HHH
HHHTHTHTTT HHH TTT
HHHTHTTHHH HHH
HHHTHTTHHT HHH
HHHTHTTHTH HHH
HHHTHTTHTT HHH
HHHTHTTTHH HHH TTT
HHHTHTTTHT HHH TTT
HHHTHTTTTH HHH TTT
HHHTHTTTTT HHH TTT
HHHTTHHHHH HHH
HHHTTHHHHT HHH
HHHTTHHHTH HHH
HHHTTHHHTT HHH
HHHTTHHTHH HHH
HHHTTHHTHT HHH
HHHTTHHTTH HHH
HHHTTHHTTT HHH TTT
HHHTTHTHHH HHH
HHHTTHTHHT HHH
HHHTTHTHTH HHH
HHHTTHTHTT HHH
HHHTTHTTHH HHH
HHHTTHTTHT HHH
HHHTTHTTTH HHH TTT
HHHTTHTTTT HHH TTT
HHHTTTHHHH HHH TTT
HHHTTTHHHT HHH TTT
HHHTTTHHTH HHH TTT
HHHTTTHHTT HHH TTT
HHHTTTHTHH HHH TTT
HHHTTTHTHT HHH TTT
HHHTTTHTTH HHH TTT
HHHTTTHTTT HHH TTT
HHHTTTTHHH HHH TTT
HHHTTTTHHT HHH TTT
HHHTTTTHTH HHH TTT
HHHTTTTHTT HHH TTT
HHHTTTTTHH HHH TTT
HHHTTTTTHT HHH TTT
HHHTTTTTTH HHH TTT
HHHTTTTTTT HHH TTT
HHTHHHHHHH HHH
HHTHHHHHHT HHH
HHTHHHHHTH HHH
HHTHHHHHTT HHH
HHTHHHHTHH HHH
HHTHHHHTHT HHH
HHTHHHHTTH HHH
HHTHHHHTTT HHH TTT
HHTHHHTHHH HHH
HHTHHHTHHT HHH
HHTHHHTHTH HHH
HHTHHHTHTT HHH
HHTHHHTTHH HHH
HHTHHHTTHT HHH
HHTHHHTTTH HHH TTT
HHTHHHTTTT HHH TTT
HHTHHTHHHH HHH
HHTHHTHHHT HHH
HHTHHTHHTH
HHTHHTHHTT
HHTHHTHTHH
HHTHHTHTHT
HHTHHTHTTH
HHTHHTHTTT TTT
HHTHHTTHHH HHH  ***
HHTHHTTHHT 
HHTHHTTHTH
HHTHHTTHTT
HHTHHTTTHH TTT
HHTHHTTTHT TTT
HHTHHTTTTH TTT
HHTHHTTTTT TTT
HHTHTHHHHH HHH
HHTHTHHHHT HHH
HHTHTHHHTH HHH
HHTHTHHHTT HHH
HHTHTHHTHH
HHTHTHHTHT
HHTHTHHTTH
HHTHTHHTTT TTT
HHTHTHTHHH HHH  ***
HHTHTHTHHT 
HHTHTHTHTH
HHTHTHTHTT
HHTHTHTTHH
HHTHTHTTHT
HHTHTHTTTH TTT
HHTHTHTTTT TTT
HHTHTTHHHH HHH
HHTHTTHHHT HHH
HHTHTTHHTH
HHTHTTHHTT
HHTHTTHTHH
HHTHTTHTHT
HHTHTTHTTH
HHTHTTHTTT TTT
HHTHTTTHHH TTT HHH
HHTHTTTHHT TTT
HHTHTTTHTH TTT
HHTHTTTHTT TTT
HHTHTTTTHH TTT
HHTHTTTTHT TTT
HHTHTTTTTH TTT
HHTHTTTTTT TTT
HHTTHHHHHH HHH
HHTTHHHHHT HHH
HHTTHHHHTH HHH
HHTTHHHHTT HHH
HHTTHHHTHH HHH
HHTTHHHTHT HHH
HHTTHHHTTH HHH
HHTTHHHTTT HHH TTT
HHTTHHTHHH HHH  ***
HHTTHHTHHT 
HHTTHHTHTH
HHTTHHTHTT
HHTTHHTTHH
HHTTHHTTHT
HHTTHHTTTH TTT
HHTTHHTTTT TTT
HHTTHTHHHH HHH
HHTTHTHHHT HHH
HHTTHTHHTH
HHTTHTHHTT
HHTTHTHTHH
HHTTHTHTHT
HHTTHTHTTH
HHTTHTHTTT TTT
HHTTHTTHHH HHH  ***
HHTTHTTHHT 
HHTTHTTHTH
HHTTHTTHTT
HHTTHTTTHH TTT
HHTTHTTTHT TTT
HHTTHTTTTH TTT
HHTTHTTTTT TTT
HHTTTHHHHH TTT HHH
HHTTTHHHHT TTT HHH
HHTTTHHHTH TTT HHH
HHTTTHHHTT TTT HHH
HHTTTHHTHH TTT
HHTTTHHTHT TTT
HHTTTHHTTH TTT
HHTTTHHTTT TTT
HHTTTHTHHH TTT HHH
HHTTTHTHHT TTT
HHTTTHTHTH TTT
HHTTTHTHTT TTT
HHTTTHTTHH TTT
HHTTTHTTHT TTT
HHTTTHTTTH TTT
HHTTTHTTTT TTT
HHTTTTHHHH TTT HHH
HHTTTTHHHT TTT HHH
HHTTTTHHTH TTT
HHTTTTHHTT TTT
HHTTTTHTHH TTT
HHTTTTHTHT TTT
HHTTTTHTTH TTT
HHTTTTHTTT TTT
HHTTTTTHHH TTT HHH
HHTTTTTHHT TTT
HHTTTTTHTH TTT
HHTTTTTHTT TTT
HHTTTTTTHH TTT
HHTTTTTTHT TTT
HHTTTTTTTH TTT
HHTTTTTTTT TTT
HTHHHHHHHH HHH
HTHHHHHHHT HHH
HTHHHHHHTH HHH
HTHHHHHHTT HHH
HTHHHHHTHH HHH
HTHHHHHTHT HHH
HTHHHHHTTH HHH
HTHHHHHTTT HHH TTT
HTHHHHTHHH HHH
HTHHHHTHHT HHH
HTHHHHTHTH HHH
HTHHHHTHTT HHH
HTHHHHTTHH HHH
HTHHHHTTHT HHH
HTHHHHTTTH HHH TTT
HTHHHHTTTT HHH TTT
HTHHHTHHHH HHH
HTHHHTHHHT HHH
HTHHHTHHTH HHH
HTHHHTHHTT HHH
HTHHHTHTHH HHH
HTHHHTHTHT HHH
HTHHHTHTTH HHH
HTHHHTHTTT HHH TTT
HTHHHTTHHH HHH
HTHHHTTHHT HHH
HTHHHTTHTH HHH
HTHHHTTHTT HHH
HTHHHTTTHH HHH TTT
HTHHHTTTHT HHH TTT
HTHHHTTTTH HHH TTT
HTHHHTTTTT HHH TTT
HTHHTHHHHH HHH
HTHHTHHHHT HHH
HTHHTHHHTH HHH
HTHHTHHHTT HHH
HTHHTHHTHH
HTHHTHHTHT
HTHHTHHTTH
HTHHTHHTTT TTT
HTHHTHTHHH HHH  ***
HTHHTHTHHT 
HTHHTHTHTH
HTHHTHTHTT
HTHHTHTTHH
HTHHTHTTHT
HTHHTHTTTH TTT
HTHHTHTTTT TTT
HTHHTTHHHH HHH
HTHHTTHHHT HHH
HTHHTTHHTH
HTHHTTHHTT
HTHHTTHTHH
HTHHTTHTHT
HTHHTTHTTH
HTHHTTHTTT TTT
HTHHTTTHHH TTT HHH
HTHHTTTHHT TTT
HTHHTTTHTH TTT
HTHHTTTHTT TTT
HTHHTTTTHH TTT
HTHHTTTTHT TTT
HTHHTTTTTH TTT
HTHHTTTTTT TTT
HTHTHHHHHH HHH
HTHTHHHHHT HHH
HTHTHHHHTH HHH
HTHTHHHHTT HHH
HTHTHHHTHH HHH
HTHTHHHTHT HHH
HTHTHHHTTH HHH
HTHTHHHTTT HHH TTT
HTHTHHTHHH HHH  ***
HTHTHHTHHT 
HTHTHHTHTH
HTHTHHTHTT
HTHTHHTTHH
HTHTHHTTHT
HTHTHHTTTH TTT
HTHTHHTTTT TTT
HTHTHTHHHH HHH
HTHTHTHHHT HHH
HTHTHTHHTH
HTHTHTHHTT
HTHTHTHTHH
HTHTHTHTHT
HTHTHTHTTH
HTHTHTHTTT TTT
HTHTHTTHHH HHH  ***
HTHTHTTHHT 
HTHTHTTHTH
HTHTHTTHTT
HTHTHTTTHH TTT
HTHTHTTTHT TTT
HTHTHTTTTH TTT
HTHTHTTTTT TTT
HTHTTHHHHH HHH
HTHTTHHHHT HHH
HTHTTHHHTH HHH
HTHTTHHHTT HHH
HTHTTHHTHH
HTHTTHHTHT
HTHTTHHTTH
HTHTTHHTTT TTT
HTHTTHTHHH HHH  ***
HTHTTHTHHT 
HTHTTHTHTH
HTHTTHTHTT
HTHTTHTTHH
HTHTTHTTHT
HTHTTHTTTH TTT
HTHTTHTTTT TTT
HTHTTTHHHH TTT HHH
HTHTTTHHHT TTT HHH
HTHTTTHHTH TTT
HTHTTTHHTT TTT
HTHTTTHTHH TTT
HTHTTTHTHT TTT
HTHTTTHTTH TTT
HTHTTTHTTT TTT
HTHTTTTHHH TTT HHH
HTHTTTTHHT TTT
HTHTTTTHTH TTT
HTHTTTTHTT TTT
HTHTTTTTHH TTT
HTHTTTTTHT TTT
HTHTTTTTTH TTT
HTHTTTTTTT TTT
HTTHHHHHHH HHH
HTTHHHHHHT HHH
HTTHHHHHTH HHH
HTTHHHHHTT HHH
HTTHHHHTHH HHH
HTTHHHHTHT HHH
HTTHHHHTTH HHH
HTTHHHHTTT HHH TTT
HTTHHHTHHH HHH
HTTHHHTHHT HHH
HTTHHHTHTH HHH
HTTHHHTHTT HHH
HTTHHHTTHH HHH
HTTHHHTTHT HHH
HTTHHHTTTH HHH TTT
HTTHHHTTTT HHH TTT
HTTHHTHHHH HHH
HTTHHTHHHT HHH
HTTHHTHHTH
HTTHHTHHTT
HTTHHTHTHH
HTTHHTHTHT
HTTHHTHTTH
HTTHHTHTTT TTT
HTTHHTTHHH HHH  ***
HTTHHTTHHT 
HTTHHTTHTH
HTTHHTTHTT
HTTHHTTTHH TTT
HTTHHTTTHT TTT
HTTHHTTTTH TTT
HTTHHTTTTT TTT
HTTHTHHHHH HHH
HTTHTHHHHT HHH
HTTHTHHHTH HHH
HTTHTHHHTT HHH
HTTHTHHTHH
HTTHTHHTHT
HTTHTHHTTH
HTTHTHHTTT TTT
HTTHTHTHHH HHH  ***
HTTHTHTHHT 
HTTHTHTHTH
HTTHTHTHTT
HTTHTHTTHH
HTTHTHTTHT
HTTHTHTTTH TTT
HTTHTHTTTT TTT
HTTHTTHHHH HHH
HTTHTTHHHT HHH
HTTHTTHHTH
HTTHTTHHTT
HTTHTTHTHH
HTTHTTHTHT
HTTHTTHTTH
HTTHTTHTTT TTT
HTTHTTTHHH TTT HHH
HTTHTTTHHT TTT
HTTHTTTHTH TTT
HTTHTTTHTT TTT
HTTHTTTTHH TTT
HTTHTTTTHT TTT
HTTHTTTTTH TTT
HTTHTTTTTT TTT
HTTTHHHHHH TTT HHH
HTTTHHHHHT TTT HHH
HTTTHHHHTH TTT HHH
HTTTHHHHTT TTT HHH
HTTTHHHTHH TTT HHH
HTTTHHHTHT TTT HHH
HTTTHHHTTH TTT HHH
HTTTHHHTTT TTT HHH
HTTTHHTHHH TTT HHH
HTTTHHTHHT TTT
HTTTHHTHTH TTT
HTTTHHTHTT TTT
HTTTHHTTHH TTT
HTTTHHTTHT TTT
HTTTHHTTTH TTT
HTTTHHTTTT TTT
HTTTHTHHHH TTT HHH
HTTTHTHHHT TTT HHH
HTTTHTHHTH TTT
HTTTHTHHTT TTT
HTTTHTHTHH TTT
HTTTHTHTHT TTT
HTTTHTHTTH TTT
HTTTHTHTTT TTT
HTTTHTTHHH TTT HHH
HTTTHTTHHT TTT
HTTTHTTHTH TTT
HTTTHTTHTT TTT
HTTTHTTTHH TTT
HTTTHTTTHT TTT
HTTTHTTTTH TTT
HTTTHTTTTT TTT
HTTTTHHHHH TTT HHH
HTTTTHHHHT TTT HHH
HTTTTHHHTH TTT HHH
HTTTTHHHTT TTT HHH
HTTTTHHTHH TTT
HTTTTHHTHT TTT
HTTTTHHTTH TTT
HTTTTHHTTT TTT
HTTTTHTHHH TTT HHH
HTTTTHTHHT TTT
HTTTTHTHTH TTT
HTTTTHTHTT TTT
HTTTTHTTHH TTT
HTTTTHTTHT TTT
HTTTTHTTTH TTT
HTTTTHTTTT TTT
HTTTTTHHHH TTT HHH
HTTTTTHHHT TTT HHH
HTTTTTHHTH TTT
HTTTTTHHTT TTT
HTTTTTHTHH TTT
HTTTTTHTHT TTT
HTTTTTHTTH TTT
HTTTTTHTTT TTT
HTTTTTTHHH TTT HHH
HTTTTTTHHT TTT
HTTTTTTHTH TTT
HTTTTTTHTT TTT
HTTTTTTTHH TTT
HTTTTTTTHT TTT
HTTTTTTTTH TTT
HTTTTTTTTT TTT
THHHHHHHHH HHH
THHHHHHHHT HHH
THHHHHHHTH HHH
THHHHHHHTT HHH
THHHHHHTHH HHH
THHHHHHTHT HHH
THHHHHHTTH HHH
THHHHHHTTT HHH TTT
THHHHHTHHH HHH
THHHHHTHHT HHH
THHHHHTHTH HHH
THHHHHTHTT HHH
THHHHHTTHH HHH
THHHHHTTHT HHH
THHHHHTTTH HHH TTT
THHHHHTTTT HHH TTT
THHHHTHHHH HHH
THHHHTHHHT HHH
THHHHTHHTH HHH
THHHHTHHTT HHH
THHHHTHTHH HHH
THHHHTHTHT HHH
THHHHTHTTH HHH
THHHHTHTTT HHH TTT
THHHHTTHHH HHH
THHHHTTHHT HHH
THHHHTTHTH HHH
THHHHTTHTT HHH
THHHHTTTHH HHH TTT
THHHHTTTHT HHH TTT
THHHHTTTTH HHH TTT
THHHHTTTTT HHH TTT
THHHTHHHHH HHH
THHHTHHHHT HHH
THHHTHHHTH HHH
THHHTHHHTT HHH
THHHTHHTHH HHH
THHHTHHTHT HHH
THHHTHHTTH HHH
THHHTHHTTT HHH TTT
THHHTHTHHH HHH
THHHTHTHHT HHH
THHHTHTHTH HHH
THHHTHTHTT HHH
THHHTHTTHH HHH
THHHTHTTHT HHH
THHHTHTTTH HHH TTT
THHHTHTTTT HHH TTT
THHHTTHHHH HHH
THHHTTHHHT HHH
THHHTTHHTH HHH
THHHTTHHTT HHH
THHHTTHTHH HHH
THHHTTHTHT HHH
THHHTTHTTH HHH
THHHTTHTTT HHH TTT
THHHTTTHHH HHH TTT
THHHTTTHHT HHH TTT
THHHTTTHTH HHH TTT
THHHTTTHTT HHH TTT
THHHTTTTHH HHH TTT
THHHTTTTHT HHH TTT
THHHTTTTTH HHH TTT
THHHTTTTTT HHH TTT
THHTHHHHHH HHH
THHTHHHHHT HHH
THHTHHHHTH HHH
THHTHHHHTT HHH
THHTHHHTHH HHH
THHTHHHTHT HHH
THHTHHHTTH HHH
THHTHHHTTT HHH TTT
THHTHHTHHH HHH  ***
THHTHHTHHT 
THHTHHTHTH
THHTHHTHTT
THHTHHTTHH
THHTHHTTHT
THHTHHTTTH TTT
THHTHHTTTT TTT
THHTHTHHHH HHH
THHTHTHHHT HHH
THHTHTHHTH
THHTHTHHTT
THHTHTHTHH
THHTHTHTHT
THHTHTHTTH
THHTHTHTTT TTT
THHTHTTHHH HHH  ***
THHTHTTHHT 
THHTHTTHTH
THHTHTTHTT
THHTHTTTHH TTT
THHTHTTTHT TTT
THHTHTTTTH TTT
THHTHTTTTT TTT
THHTTHHHHH HHH
THHTTHHHHT HHH
THHTTHHHTH HHH
THHTTHHHTT HHH
THHTTHHTHH
THHTTHHTHT
THHTTHHTTH
THHTTHHTTT TTT
THHTTHTHHH HHH  ***
THHTTHTHHT 
THHTTHTHTH
THHTTHTHTT
THHTTHTTHH
THHTTHTTHT
THHTTHTTTH TTT
THHTTHTTTT TTT
THHTTTHHHH TTT HHH
THHTTTHHHT TTT HHH
THHTTTHHTH TTT
THHTTTHHTT TTT
THHTTTHTHH TTT
THHTTTHTHT TTT
THHTTTHTTH TTT
THHTTTHTTT TTT
THHTTTTHHH TTT HHH
THHTTTTHHT TTT
THHTTTTHTH TTT
THHTTTTHTT TTT
THHTTTTTHH TTT
THHTTTTTHT TTT
THHTTTTTTH TTT
THHTTTTTTT TTT
THTHHHHHHH HHH
THTHHHHHHT HHH
THTHHHHHTH HHH
THTHHHHHTT HHH
THTHHHHTHH HHH
THTHHHHTHT HHH
THTHHHHTTH HHH
THTHHHHTTT HHH TTT
THTHHHTHHH HHH
THTHHHTHHT HHH
THTHHHTHTH HHH
THTHHHTHTT HHH
THTHHHTTHH HHH
THTHHHTTHT HHH
THTHHHTTTH HHH TTT
THTHHHTTTT HHH TTT
THTHHTHHHH HHH
THTHHTHHHT HHH
THTHHTHHTH
THTHHTHHTT
THTHHTHTHH
THTHHTHTHT
THTHHTHTTH
THTHHTHTTT TTT
THTHHTTHHH HHH  ***
THTHHTTHHT 
THTHHTTHTH
THTHHTTHTT
THTHHTTTHH TTT
THTHHTTTHT TTT
THTHHTTTTH TTT
THTHHTTTTT TTT
THTHTHHHHH HHH
THTHTHHHHT HHH
THTHTHHHTH HHH
THTHTHHHTT HHH
THTHTHHTHH
THTHTHHTHT
THTHTHHTTH
THTHTHHTTT TTT
THTHTHTHHH HHH  ***
THTHTHTHHT 
THTHTHTHTH
THTHTHTHTT
THTHTHTTHH
THTHTHTTHT
THTHTHTTTH TTT
THTHTHTTTT TTT
THTHTTHHHH HHH
THTHTTHHHT HHH
THTHTTHHTH
THTHTTHHTT
THTHTTHTHH
THTHTTHTHT
THTHTTHTTH
THTHTTHTTT TTT
THTHTTTHHH TTT HHH
THTHTTTHHT TTT
THTHTTTHTH TTT
THTHTTTHTT TTT
THTHTTTTHH TTT
THTHTTTTHT TTT
THTHTTTTTH TTT
THTHTTTTTT TTT
THTTHHHHHH HHH
THTTHHHHHT HHH
THTTHHHHTH HHH
THTTHHHHTT HHH
THTTHHHTHH HHH
THTTHHHTHT HHH
THTTHHHTTH HHH
THTTHHHTTT HHH TTT
THTTHHTHHH HHH  ***
THTTHHTHHT 
THTTHHTHTH
THTTHHTHTT
THTTHHTTHH
THTTHHTTHT
THTTHHTTTH TTT
THTTHHTTTT TTT
THTTHTHHHH HHH
THTTHTHHHT HHH
THTTHTHHTH
THTTHTHHTT
THTTHTHTHH
THTTHTHTHT
THTTHTHTTH
THTTHTHTTT TTT
THTTHTTHHH HHH  ***
THTTHTTHHT 
THTTHTTHTH
THTTHTTHTT
THTTHTTTHH TTT
THTTHTTTHT TTT
THTTHTTTTH TTT
THTTHTTTTT TTT
THTTTHHHHH TTT HHH
THTTTHHHHT TTT HHH
THTTTHHHTH TTT HHH
THTTTHHHTT TTT HHH
THTTTHHTHH TTT
THTTTHHTHT TTT
THTTTHHTTH TTT
THTTTHHTTT TTT
THTTTHTHHH TTT HHH
THTTTHTHHT TTT
THTTTHTHTH TTT
THTTTHTHTT TTT
THTTTHTTHH TTT
THTTTHTTHT TTT
THTTTHTTTH TTT
THTTTHTTTT TTT
THTTTTHHHH TTT HHH
THTTTTHHHT TTT HHH
THTTTTHHTH TTT
THTTTTHHTT TTT
THTTTTHTHH TTT
THTTTTHTHT TTT
THTTTTHTTH TTT
THTTTTHTTT TTT
THTTTTTHHH TTT HHH
THTTTTTHHT TTT
THTTTTTHTH TTT
THTTTTTHTT TTT
THTTTTTTHH TTT
THTTTTTTHT TTT
THTTTTTTTH TTT
THTTTTTTTT TTT
TTHHHHHHHH HHH
TTHHHHHHHT HHH
TTHHHHHHTH HHH
TTHHHHHHTT HHH
TTHHHHHTHH HHH
TTHHHHHTHT HHH
TTHHHHHTTH HHH
TTHHHHHTTT HHH TTT
TTHHHHTHHH HHH
TTHHHHTHHT HHH
TTHHHHTHTH HHH
TTHHHHTHTT HHH
TTHHHHTTHH HHH
TTHHHHTTHT HHH
TTHHHHTTTH HHH TTT
TTHHHHTTTT HHH TTT
TTHHHTHHHH HHH
TTHHHTHHHT HHH
TTHHHTHHTH HHH
TTHHHTHHTT HHH
TTHHHTHTHH HHH
TTHHHTHTHT HHH
TTHHHTHTTH HHH
TTHHHTHTTT HHH TTT
TTHHHTTHHH HHH
TTHHHTTHHT HHH
TTHHHTTHTH HHH
TTHHHTTHTT HHH
TTHHHTTTHH HHH TTT
TTHHHTTTHT HHH TTT
TTHHHTTTTH HHH TTT
TTHHHTTTTT HHH TTT
TTHHTHHHHH HHH
TTHHTHHHHT HHH
TTHHTHHHTH HHH
TTHHTHHHTT HHH
TTHHTHHTHH
TTHHTHHTHT
TTHHTHHTTH
TTHHTHHTTT TTT
TTHHTHTHHH HHH  ***
TTHHTHTHHT 
TTHHTHTHTH
TTHHTHTHTT
TTHHTHTTHH
TTHHTHTTHT
TTHHTHTTTH TTT
TTHHTHTTTT TTT
TTHHTTHHHH HHH
TTHHTTHHHT HHH
TTHHTTHHTH
TTHHTTHHTT
TTHHTTHTHH
TTHHTTHTHT
TTHHTTHTTH
TTHHTTHTTT TTT
TTHHTTTHHH TTT HHH
TTHHTTTHHT TTT
TTHHTTTHTH TTT
TTHHTTTHTT TTT
TTHHTTTTHH TTT
TTHHTTTTHT TTT
TTHHTTTTTH TTT
TTHHTTTTTT TTT
TTHTHHHHHH HHH
TTHTHHHHHT HHH
TTHTHHHHTH HHH
TTHTHHHHTT HHH
TTHTHHHTHH HHH
TTHTHHHTHT HHH
TTHTHHHTTH HHH
TTHTHHHTTT HHH TTT
TTHTHHTHHH HHH  ***
TTHTHHTHHT 
TTHTHHTHTH
TTHTHHTHTT
TTHTHHTTHH
TTHTHHTTHT
TTHTHHTTTH TTT
TTHTHHTTTT TTT
TTHTHTHHHH HHH
TTHTHTHHHT HHH
TTHTHTHHTH
TTHTHTHHTT
TTHTHTHTHH
TTHTHTHTHT
TTHTHTHTTH
TTHTHTHTTT TTT
TTHTHTTHHH HHH  ***
TTHTHTTHHT 
TTHTHTTHTH
TTHTHTTHTT
TTHTHTTTHH TTT
TTHTHTTTHT TTT
TTHTHTTTTH TTT
TTHTHTTTTT TTT
TTHTTHHHHH HHH
TTHTTHHHHT HHH
TTHTTHHHTH HHH
TTHTTHHHTT HHH
TTHTTHHTHH
TTHTTHHTHT
TTHTTHHTTH
TTHTTHHTTT TTT
TTHTTHTHHH HHH  ***
TTHTTHTHHT 
TTHTTHTHTH
TTHTTHTHTT
TTHTTHTTHH
TTHTTHTTHT
TTHTTHTTTH TTT
TTHTTHTTTT TTT
TTHTTTHHHH TTT HHH
TTHTTTHHHT TTT HHH
TTHTTTHHTH TTT
TTHTTTHHTT TTT
TTHTTTHTHH TTT
TTHTTTHTHT TTT
TTHTTTHTTH TTT
TTHTTTHTTT TTT
TTHTTTTHHH TTT HHH
TTHTTTTHHT TTT
TTHTTTTHTH TTT
TTHTTTTHTT TTT
TTHTTTTTHH TTT
TTHTTTTTHT TTT
TTHTTTTTTH TTT
TTHTTTTTTT TTT
TTTHHHHHHH TTT HHH
TTTHHHHHHT TTT HHH
TTTHHHHHTH TTT HHH
TTTHHHHHTT TTT HHH
TTTHHHHTHH TTT HHH
TTTHHHHTHT TTT HHH
TTTHHHHTTH TTT HHH
TTTHHHHTTT TTT HHH
TTTHHHTHHH TTT HHH
TTTHHHTHHT TTT HHH
TTTHHHTHTH TTT HHH
TTTHHHTHTT TTT HHH
TTTHHHTTHH TTT HHH
TTTHHHTTHT TTT HHH
TTTHHHTTTH TTT HHH
TTTHHHTTTT TTT HHH
TTTHHTHHHH TTT HHH
TTTHHTHHHT TTT HHH
TTTHHTHHTH TTT
TTTHHTHHTT TTT
TTTHHTHTHH TTT
TTTHHTHTHT TTT
TTTHHTHTTH TTT
TTTHHTHTTT TTT
TTTHHTTHHH TTT HHH
TTTHHTTHHT TTT
TTTHHTTHTH TTT
TTTHHTTHTT TTT
TTTHHTTTHH TTT
TTTHHTTTHT TTT
TTTHHTTTTH TTT
TTTHHTTTTT TTT
TTTHTHHHHH TTT HHH
TTTHTHHHHT TTT HHH
TTTHTHHHTH TTT HHH
TTTHTHHHTT TTT HHH
TTTHTHHTHH TTT
TTTHTHHTHT TTT
TTTHTHHTTH TTT
TTTHTHHTTT TTT
TTTHTHTHHH TTT HHH
TTTHTHTHHT TTT
TTTHTHTHTH TTT
TTTHTHTHTT TTT
TTTHTHTTHH TTT
TTTHTHTTHT TTT
TTTHTHTTTH TTT
TTTHTHTTTT TTT
TTTHTTHHHH TTT HHH
TTTHTTHHHT TTT HHH
TTTHTTHHTH TTT
TTTHTTHHTT TTT
TTTHTTHTHH TTT
TTTHTTHTHT TTT
TTTHTTHTTH TTT
TTTHTTHTTT TTT
TTTHTTTHHH TTT HHH
TTTHTTTHHT TTT
TTTHTTTHTH TTT
TTTHTTTHTT TTT
TTTHTTTTHH TTT
TTTHTTTTHT TTT
TTTHTTTTTH TTT
TTTHTTTTTT TTT
TTTTHHHHHH TTT HHH
TTTTHHHHHT TTT HHH
TTTTHHHHTH TTT HHH
TTTTHHHHTT TTT HHH
TTTTHHHTHH TTT HHH
TTTTHHHTHT TTT HHH
TTTTHHHTTH TTT HHH
TTTTHHHTTT TTT HHH
TTTTHHTHHH TTT HHH
TTTTHHTHHT TTT
TTTTHHTHTH TTT
TTTTHHTHTT TTT
TTTTHHTTHH TTT
TTTTHHTTHT TTT
TTTTHHTTTH TTT
TTTTHHTTTT TTT
TTTTHTHHHH TTT HHH
TTTTHTHHHT TTT HHH
TTTTHTHHTH TTT
TTTTHTHHTT TTT
TTTTHTHTHH TTT
TTTTHTHTHT TTT
TTTTHTHTTH TTT
TTTTHTHTTT TTT
TTTTHTTHHH TTT HHH
TTTTHTTHHT TTT
TTTTHTTHTH TTT
TTTTHTTHTT TTT
TTTTHTTTHH TTT
TTTTHTTTHT TTT
TTTTHTTTTH TTT
TTTTHTTTTT TTT
TTTTTHHHHH TTT HHH
TTTTTHHHHT TTT HHH
TTTTTHHHTH TTT HHH
TTTTTHHHTT TTT HHH
TTTTTHHTHH TTT
TTTTTHHTHT TTT
TTTTTHHTTH TTT
TTTTTHHTTT TTT
TTTTTHTHHH TTT HHH
TTTTTHTHHT TTT
TTTTTHTHTH TTT
TTTTTHTHTT TTT
TTTTTHTTHH TTT
TTTTTHTTHT TTT
TTTTTHTTTH TTT
TTTTTHTTTT TTT
TTTTTTHHHH TTT HHH
TTTTTTHHHT TTT HHH
TTTTTTHHTH TTT
TTTTTTHHTT TTT
TTTTTTHTHH TTT
TTTTTTHTHT TTT
TTTTTTHTTH TTT
TTTTTTHTTT TTT
TTTTTTTHHH TTT HHH
TTTTTTTHHT TTT
TTTTTTTHTH TTT
TTTTTTTHTT TTT
TTTTTTTTHH TTT
TTTTTTTTHT TTT
TTTTTTTTTH TTT
TTTTTTTTTT TTT

TTT only 326 ; HHH only 326  (as last 21 ); TTT bef HHH 97 ; HHH bef TTT 97 ; neither 178

The cases under consideration are those where TTT did not occur and HHH did not occur before positions 8-10. This is 178+21=199.

Out of those cases 178 did not have HHH.  That makes the probability 178/199 that you did not have 3 heads in a row either, or 89.4%, not 29.6%.

Edited on June 15, 2004, 2:06 pm
  Posted by Charlie on 2004-06-15 13:06:13

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