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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?

  Submitted by Federico Kereki    
Rating: 3.6667 (6 votes)
Solution: (Hide)
10 times; the odds are TRI(n)/2^n, which for n=10 is 504/1024, about 50%.

TRI(n) is the Fibonacci-like series defined by TRI(i)=2^i for i=0 to 2, and TRI(i)=TRI(i-3)+TRI(i-2)+TRI(i-1) for i=3 or greater.

For the second question, see the comments.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2024-01-11 11:13:09
SolutionsimulationsCharlie2004-06-17 11:12:25
SolutionThe first part now, re: Now that I know...Charlie2004-06-17 08:51:29
SolutionNow that I know...Charlie2004-06-16 21:04:17
Answer to the second questionRuopeng Wang2004-06-16 11:11:29
Solution?Ruopeng Wang2004-06-16 10:57:59
re(5): Markov chain solution - 2nd partCharlie2004-06-15 13:06:13
re(4): Markov chain solution - 2nd partFederico Kereki2004-06-15 10:43:45
re: Technically SpeakingCharlie2004-06-14 22:39:15
Technically SpeakingJeremiah2004-06-14 21:14:37
Solutionre: Markov chain solution - 2nd partCharlie2004-06-13 13:49:52
re: Exhaustion--1st and 2nd questions--the programCharlie2004-06-13 11:53:37
SolutionExhaustion--1st and 2nd questionsCharlie2004-06-13 11:25:55
re(3): Markov chain solution - 2nd partCharlie2004-06-13 10:32:10
Some Thoughtsre(2): Markov chain solution - 2nd partOskar2004-06-13 10:24:11
re: Markov chain solution - 2nd partCharlie2004-06-13 00:40:26
SolutionMarkov chain solution - 2nd partOskar2004-06-12 23:09:11
SolutionMarkov chain solution - 1st partOskar2004-06-12 23:04:29
Some ThoughtsMarkov chain solutionOskar2004-06-12 22:55:14
re(2): solutionCharlie2004-06-12 10:15:33
Some Thoughtsre: solutionOskar2004-06-12 00:04:51
dratrixar2004-06-11 18:30:16
simpleton's guessrixar2004-06-11 18:23:13
SolutionsolutionCharlie2004-06-11 15:50:05
Some ThoughtsSolutionNick Hobson2004-06-11 15:43:57
SolutionSolution?Erik O.2004-06-11 14:12:46
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