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 Coin tossing (Posted on 2004-06-11)
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 TTTHHHHHHTHHH HHH HHHHHHTHHT HHH HHHHHHTHTH HHH HHHHHHTHTT HHH HHHHHHTTHH HHH HHHHHHTTHT HHH HHHHHHTTTH HHH TTTHHHHHHTTTT HHH TTTHHHHHTHHHH HHH HHHHHTHHHT HHH HHHHHTHHTH HHH HHHHHTHHTT HHH HHHHHTHTHH HHH HHHHHTHTHT HHH HHHHHTHTTH HHH HHHHHTHTTT HHH TTTHHHHHTTHHH HHH HHHHHTTHHT HHH HHHHHTTHTH HHH HHHHHTTHTT HHH HHHHHTTTHH HHH TTTHHHHHTTTHT HHH TTTHHHHHTTTTH HHH TTTHHHHHTTTTT HHH TTTHHHHTHHHHH HHH HHHHTHHHHT HHH HHHHTHHHTH HHH HHHHTHHHTT HHH HHHHTHHTHH HHH HHHHTHHTHT HHH HHHHTHHTTH HHH HHHHTHHTTT HHH TTTHHHHTHTHHH HHH HHHHTHTHHT HHH HHHHTHTHTH HHH HHHHTHTHTT HHH HHHHTHTTHH HHH HHHHTHTTHT HHH HHHHTHTTTH HHH TTTHHHHTHTTTT HHH TTTHHHHTTHHHH HHH HHHHTTHHHT HHH HHHHTTHHTH HHH HHHHTTHHTT HHH HHHHTTHTHH HHH HHHHTTHTHT HHH HHHHTTHTTH HHH HHHHTTHTTT HHH TTTHHHHTTTHHH HHH TTTHHHHTTTHHT HHH TTTHHHHTTTHTH HHH TTTHHHHTTTHTT HHH TTTHHHHTTTTHH HHH TTTHHHHTTTTHT HHH TTTHHHHTTTTTH HHH TTTHHHHTTTTTT HHH TTTHHHTHHHHHH HHH HHHTHHHHHT HHH HHHTHHHHTH HHH HHHTHHHHTT HHH HHHTHHHTHH HHH HHHTHHHTHT HHH HHHTHHHTTH HHH HHHTHHHTTT HHH TTTHHHTHHTHHH HHH HHHTHHTHHT HHH HHHTHHTHTH HHH HHHTHHTHTT HHH HHHTHHTTHH HHH HHHTHHTTHT HHH HHHTHHTTTH HHH TTTHHHTHHTTTT HHH TTTHHHTHTHHHH HHH HHHTHTHHHT HHH HHHTHTHHTH HHH HHHTHTHHTT HHH HHHTHTHTHH HHH HHHTHTHTHT HHH HHHTHTHTTH HHH HHHTHTHTTT HHH TTTHHHTHTTHHH HHH HHHTHTTHHT HHH HHHTHTTHTH HHH HHHTHTTHTT HHH HHHTHTTTHH HHH TTTHHHTHTTTHT HHH TTTHHHTHTTTTH HHH TTTHHHTHTTTTT HHH TTTHHHTTHHHHH HHH HHHTTHHHHT HHH HHHTTHHHTH HHH HHHTTHHHTT HHH HHHTTHHTHH HHH HHHTTHHTHT HHH HHHTTHHTTH HHH HHHTTHHTTT HHH TTTHHHTTHTHHH HHH HHHTTHTHHT HHH HHHTTHTHTH HHH HHHTTHTHTT HHH HHHTTHTTHH HHH HHHTTHTTHT HHH HHHTTHTTTH HHH TTTHHHTTHTTTT HHH TTTHHHTTTHHHH HHH TTTHHHTTTHHHT HHH TTTHHHTTTHHTH HHH TTTHHHTTTHHTT HHH TTTHHHTTTHTHH HHH TTTHHHTTTHTHT HHH TTTHHHTTTHTTH HHH TTTHHHTTTHTTT HHH TTTHHHTTTTHHH HHH TTTHHHTTTTHHT HHH TTTHHHTTTTHTH HHH TTTHHHTTTTHTT HHH TTTHHHTTTTTHH HHH TTTHHHTTTTTHT HHH TTTHHHTTTTTTH HHH TTTHHHTTTTTTT HHH TTTHHTHHHHHHH HHH HHTHHHHHHT HHH HHTHHHHHTH HHH HHTHHHHHTT HHH HHTHHHHTHH HHH HHTHHHHTHT HHH HHTHHHHTTH HHH HHTHHHHTTT HHH TTTHHTHHHTHHH HHH HHTHHHTHHT HHH HHTHHHTHTH HHH HHTHHHTHTT HHH HHTHHHTTHH HHH HHTHHHTTHT HHH HHTHHHTTTH HHH TTTHHTHHHTTTT HHH TTTHHTHHTHHHH 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 HHHHHTHTTTHHT 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 TTTHHTTHHTHHH 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 HHHHHTTTHHHHT TTT HHHHHTTTHHHTH TTT HHHHHTTTHHHTT TTT HHHHHTTTHHTHH TTT HHTTTHHTHT TTT HHTTTHHTTH TTT HHTTTHHTTT TTT HHTTTHTHHH TTT HHHHHTTTHTHHT TTT HHTTTHTHTH TTT HHTTTHTHTT TTT HHTTTHTTHH TTT HHTTTHTTHT TTT HHTTTHTTTH TTT HHTTTHTTTT TTT HHTTTTHHHH TTT HHHHHTTTTHHHT TTT HHHHHTTTTHHTH TTT HHTTTTHHTT TTT HHTTTTHTHH TTT HHTTTTHTHT TTT HHTTTTHTTH TTT HHTTTTHTTT TTT HHTTTTTHHH TTT HHHHHTTTTTHHT 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 TTTHTHHHHTHHH HHH HTHHHHTHHT HHH HTHHHHTHTH HHH HTHHHHTHTT HHH HTHHHHTTHH HHH HTHHHHTTHT HHH HTHHHHTTTH HHH TTTHTHHHHTTTT HHH TTTHTHHHTHHHH HHH HTHHHTHHHT HHH HTHHHTHHTH HHH HTHHHTHHTT HHH HTHHHTHTHH HHH HTHHHTHTHT HHH HTHHHTHTTH HHH HTHHHTHTTT HHH TTTHTHHHTTHHH HHH HTHHHTTHHT HHH HTHHHTTHTH HHH HTHHHTTHTT HHH HTHHHTTTHH HHH TTTHTHHHTTTHT HHH TTTHTHHHTTTTH HHH TTTHTHHHTTTTT HHH TTTHTHHTHHHHH 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 HHHHTHHTTTHHT 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 TTTHTHTHHTHHH 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 HHHHTHTTTHHHT TTT HHHHTHTTTHHTH TTT HTHTTTHHTT TTT HTHTTTHTHH TTT HTHTTTHTHT TTT HTHTTTHTTH TTT HTHTTTHTTT TTT HTHTTTTHHH TTT HHHHTHTTTTHHT 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 TTTHTTHHHTHHH HHH HTTHHHTHHT HHH HTTHHHTHTH HHH HTTHHHTHTT HHH HTTHHHTTHH HHH HTTHHHTTHT HHH HTTHHHTTTH HHH TTTHTTHHHTTTT HHH TTTHTTHHTHHHH 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 HHHHTTHTTTHHT TTT HTTHTTTHTH TTT HTTHTTTHTT TTT HTTHTTTTHH TTT HTTHTTTTHT TTT HTTHTTTTTH TTT HTTHTTTTTT TTT HTTTHHHHHH TTT HHHHTTTHHHHHT TTT HHHHTTTHHHHTH TTT HHHHTTTHHHHTT TTT HHHHTTTHHHTHH TTT HHHHTTTHHHTHT TTT HHHHTTTHHHTTH TTT HHHHTTTHHHTTT TTT HHHHTTTHHTHHH TTT HHHHTTTHHTHHT TTT HTTTHHTHTH TTT HTTTHHTHTT TTT HTTTHHTTHH TTT HTTTHHTTHT TTT HTTTHHTTTH TTT HTTTHHTTTT TTT HTTTHTHHHH TTT HHHHTTTHTHHHT TTT HHHHTTTHTHHTH TTT HTTTHTHHTT TTT HTTTHTHTHH TTT HTTTHTHTHT TTT HTTTHTHTTH TTT HTTTHTHTTT TTT HTTTHTTHHH TTT HHHHTTTHTTHHT TTT HTTTHTTHTH TTT HTTTHTTHTT TTT HTTTHTTTHH TTT HTTTHTTTHT TTT HTTTHTTTTH TTT HTTTHTTTTT TTT HTTTTHHHHH TTT HHHHTTTTHHHHT TTT HHHHTTTTHHHTH TTT HHHHTTTTHHHTT TTT HHHHTTTTHHTHH TTT HTTTTHHTHT TTT HTTTTHHTTH TTT HTTTTHHTTT TTT HTTTTHTHHH TTT HHHHTTTTHTHHT TTT HTTTTHTHTH TTT HTTTTHTHTT TTT HTTTTHTTHH TTT HTTTTHTTHT TTT HTTTTHTTTH TTT HTTTTHTTTT TTT HTTTTTHHHH TTT HHHHTTTTTHHHT TTT HHHHTTTTTHHTH TTT HTTTTTHHTT TTT HTTTTTHTHH TTT HTTTTTHTHT TTT HTTTTTHTTH TTT HTTTTTHTTT TTT HTTTTTTHHH TTT HHHHTTTTTTHHT 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 TTTTHHHHHTHHH HHH THHHHHTHHT HHH THHHHHTHTH HHH THHHHHTHTT HHH THHHHHTTHH HHH THHHHHTTHT HHH THHHHHTTTH HHH TTTTHHHHHTTTT HHH TTTTHHHHTHHHH HHH THHHHTHHHT HHH THHHHTHHTH HHH THHHHTHHTT HHH THHHHTHTHH HHH THHHHTHTHT HHH THHHHTHTTH HHH THHHHTHTTT HHH TTTTHHHHTTHHH HHH THHHHTTHHT HHH THHHHTTHTH HHH THHHHTTHTT HHH THHHHTTTHH HHH TTTTHHHHTTTHT HHH TTTTHHHHTTTTH HHH TTTTHHHHTTTTT HHH TTTTHHHTHHHHH HHH THHHTHHHHT HHH THHHTHHHTH HHH THHHTHHHTT HHH THHHTHHTHH HHH THHHTHHTHT HHH THHHTHHTTH HHH THHHTHHTTT HHH TTTTHHHTHTHHH HHH THHHTHTHHT HHH THHHTHTHTH HHH THHHTHTHTT HHH THHHTHTTHH HHH THHHTHTTHT HHH THHHTHTTTH HHH TTTTHHHTHTTTT HHH TTTTHHHTTHHHH HHH THHHTTHHHT HHH THHHTTHHTH HHH THHHTTHHTT HHH THHHTTHTHH HHH THHHTTHTHT HHH THHHTTHTTH HHH THHHTTHTTT HHH TTTTHHHTTTHHH HHH TTTTHHHTTTHHT HHH TTTTHHHTTTHTH HHH TTTTHHHTTTHTT HHH TTTTHHHTTTTHH HHH TTTTHHHTTTTHT HHH TTTTHHHTTTTTH HHH TTTTHHHTTTTTT HHH TTTTHHTHHHHHH HHH THHTHHHHHT HHH THHTHHHHTH HHH THHTHHHHTT HHH THHTHHHTHH HHH THHTHHHTHT HHH THHTHHHTTH HHH THHTHHHTTT HHH TTTTHHTHHTHHH 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 HHHTHHTTTHHHT TTT HHHTHHTTTHHTH TTT THHTTTHHTT TTT THHTTTHTHH TTT THHTTTHTHT TTT THHTTTHTTH TTT THHTTTHTTT TTT THHTTTTHHH TTT HHHTHHTTTTHHT 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 TTTTHTHHHTHHH HHH THTHHHTHHT HHH THTHHHTHTH HHH THTHHHTHTT HHH THTHHHTTHH HHH THTHHHTTHT HHH THTHHHTTTH HHH TTTTHTHHHTTTT HHH TTTTHTHHTHHHH 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 HHHTHTHTTTHHT 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 TTTTHTTHHTHHH 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 HHHTHTTTHHHHT TTT HHHTHTTTHHHTH TTT HHHTHTTTHHHTT TTT HHHTHTTTHHTHH TTT THTTTHHTHT TTT THTTTHHTTH TTT THTTTHHTTT TTT THTTTHTHHH TTT HHHTHTTTHTHHT TTT THTTTHTHTH TTT THTTTHTHTT TTT THTTTHTTHH TTT THTTTHTTHT TTT THTTTHTTTH TTT THTTTHTTTT TTT THTTTTHHHH TTT HHHTHTTTTHHHT TTT HHHTHTTTTHHTH TTT THTTTTHHTT TTT THTTTTHTHH TTT THTTTTHTHT TTT THTTTTHTTH TTT THTTTTHTTT TTT THTTTTTHHH TTT HHHTHTTTTTHHT 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 TTTTTHHHHTHHH HHH TTHHHHTHHT HHH TTHHHHTHTH HHH TTHHHHTHTT HHH TTHHHHTTHH HHH TTHHHHTTHT HHH TTHHHHTTTH HHH TTTTTHHHHTTTT HHH TTTTTHHHTHHHH HHH TTHHHTHHHT HHH TTHHHTHHTH HHH TTHHHTHHTT HHH TTHHHTHTHH HHH TTHHHTHTHT HHH TTHHHTHTTH HHH TTHHHTHTTT HHH TTTTTHHHTTHHH HHH TTHHHTTHHT HHH TTHHHTTHTH HHH TTHHHTTHTT HHH TTHHHTTTHH HHH TTTTTHHHTTTHT HHH TTTTTHHHTTTTH HHH TTTTTHHHTTTTT HHH TTTTTHHTHHHHH 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 HHHTTHHTTTHHT 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 TTTTTHTHHTHHH 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 HHHTTHTTTHHHT TTT HHHTTHTTTHHTH TTT TTHTTTHHTT TTT TTHTTTHTHH TTT TTHTTTHTHT TTT TTHTTTHTTH TTT TTHTTTHTTT TTT TTHTTTTHHH TTT HHHTTHTTTTHHT TTT TTHTTTTHTH TTT TTHTTTTHTT TTT TTHTTTTTHH TTT TTHTTTTTHT TTT TTHTTTTTTH TTT TTHTTTTTTT TTT TTTHHHHHHH TTT HHHTTTHHHHHHT TTT HHHTTTHHHHHTH TTT HHHTTTHHHHHTT TTT HHHTTTHHHHTHH TTT HHHTTTHHHHTHT TTT HHHTTTHHHHTTH TTT HHHTTTHHHHTTT TTT HHHTTTHHHTHHH TTT HHHTTTHHHTHHT TTT HHHTTTHHHTHTH TTT HHHTTTHHHTHTT TTT HHHTTTHHHTTHH TTT HHHTTTHHHTTHT TTT HHHTTTHHHTTTH TTT HHHTTTHHHTTTT TTT HHHTTTHHTHHHH TTT HHHTTTHHTHHHT TTT HHHTTTHHTHHTH TTT TTTHHTHHTT TTT TTTHHTHTHH TTT TTTHHTHTHT TTT TTTHHTHTTH TTT TTTHHTHTTT TTT TTTHHTTHHH TTT HHHTTTHHTTHHT TTT TTTHHTTHTH TTT TTTHHTTHTT TTT TTTHHTTTHH TTT TTTHHTTTHT TTT TTTHHTTTTH TTT TTTHHTTTTT TTT TTTHTHHHHH TTT HHHTTTHTHHHHT TTT HHHTTTHTHHHTH TTT HHHTTTHTHHHTT TTT HHHTTTHTHHTHH TTT TTTHTHHTHT TTT TTTHTHHTTH TTT TTTHTHHTTT TTT TTTHTHTHHH TTT HHHTTTHTHTHHT TTT TTTHTHTHTH TTT TTTHTHTHTT TTT TTTHTHTTHH TTT TTTHTHTTHT TTT TTTHTHTTTH TTT TTTHTHTTTT TTT TTTHTTHHHH TTT HHHTTTHTTHHHT TTT HHHTTTHTTHHTH TTT TTTHTTHHTT TTT TTTHTTHTHH TTT TTTHTTHTHT TTT TTTHTTHTTH TTT TTTHTTHTTT TTT TTTHTTTHHH TTT HHHTTTHTTTHHT TTT TTTHTTTHTH TTT TTTHTTTHTT TTT TTTHTTTTHH TTT TTTHTTTTHT TTT TTTHTTTTTH TTT TTTHTTTTTT TTT TTTTHHHHHH TTT HHHTTTTHHHHHT TTT HHHTTTTHHHHTH TTT HHHTTTTHHHHTT TTT HHHTTTTHHHTHH TTT HHHTTTTHHHTHT TTT HHHTTTTHHHTTH TTT HHHTTTTHHHTTT TTT HHHTTTTHHTHHH TTT HHHTTTTHHTHHT TTT TTTTHHTHTH TTT TTTTHHTHTT TTT TTTTHHTTHH TTT TTTTHHTTHT TTT TTTTHHTTTH TTT TTTTHHTTTT TTT TTTTHTHHHH TTT HHHTTTTHTHHHT TTT HHHTTTTHTHHTH TTT TTTTHTHHTT TTT TTTTHTHTHH TTT TTTTHTHTHT TTT TTTTHTHTTH TTT TTTTHTHTTT TTT TTTTHTTHHH TTT HHHTTTTHTTHHT TTT TTTTHTTHTH TTT TTTTHTTHTT TTT TTTTHTTTHH TTT TTTTHTTTHT TTT TTTTHTTTTH TTT TTTTHTTTTT TTT TTTTTHHHHH TTT HHHTTTTTHHHHT TTT HHHTTTTTHHHTH TTT HHHTTTTTHHHTT TTT HHHTTTTTHHTHH TTT TTTTTHHTHT TTT TTTTTHHTTH TTT TTTTTHHTTT TTT TTTTTHTHHH TTT HHHTTTTTHTHHT TTT TTTTTHTHTH TTT TTTTTHTHTT TTT TTTTTHTTHH TTT TTTTTHTTHT TTT TTTTTHTTTH TTT TTTTTHTTTT TTT TTTTTTHHHH TTT HHHTTTTTTHHHT TTT HHHTTTTTTHHTH TTT TTTTTTHHTT TTT TTTTTTHTHH TTT TTTTTTHTHT TTT TTTTTTHTTH TTT TTTTTTHTTT TTT TTTTTTTHHH TTT HHHTTTTTTTHHT 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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