A probability theory question which I came across lately and where the answer unexpectedly turned out to be not so easy?!Given a perfect coin. Throw the coin 12 times. Have a look at the longest "trend", that is the biggest number of consecutive throws that have the same outcome. Example: abaabbbababa (longest trend = 3)What is the probability that a) the longest trend when throwing 12 times is AT LEAST x throws long (x=1,...,12)?b) the longest trend when throwing 12 times is EXACTLY x throws long (x=1,...,12)?Any suggestions hwo to generalize this to a variable number of throws?

I don't have a comment on the problem but I do have a comment on this site.Perhaps it would work best if people posted (where possible) to subsections directly relevant to their queries?For example, if we posted brainteasers and probability problems in the brainteaser section?Just a suggestion but I think it would help everyone navigate this resource better.FirstQuantJob

QuoteOriginally posted by: FirstQuantJobI don't have a comment on the problem but I do have a comment on this site.Perhaps it would work best if people posted (where possible) to subsections directly relevant to their queries?For example, if we posted brainteasers and probability problems in the brainteaser section?Just a suggestion but I think it would help everyone navigate this resource better.perhaps your suggestion (and mine) belongs in "Forum and Website Bugs and Suggestions" ?

Not sure about (a). Couldn't you solve (b) using discrete time Markov chain of two states? State 1 = result is same as last toss). State 2 = result is different than last toss. Thought I saw something kind of like this solved in a class I took once.

QuoteOriginally posted by: ppauperQuoteOriginally posted by: FirstQuantJobI don't have a comment on the problem but I do have a comment on this site.Perhaps it would work best if people posted (where possible) to subsections directly relevant to their queries?For example, if we posted brainteasers and probability problems in the brainteaser section?Just a suggestion but I think it would help everyone navigate this resource better.perhaps your suggestion (and mine) belongs in "Forum and Website Bugs and Suggestions" ?Good advice ppauper! See my recent posting in that forum -- "Posting to relevant section of site".I discuss how the site could be slightly redesigned along the above lines.FirstQuantJob