4 ms·
"If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require fo
by jamieb007 11y ago
"If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses."
Counter-intuitive at first but makes sense - the outcomes as a whole converge towards the average (50% heads, 50% tails). Nonetheless, it shows that each toss is related to the others. One can expect that primes are even more related - or at least to the primes that came before.
- hmate9 11y agoThat is a really fun little puzzle and you're right, it seemed completely counter intuitive at first sight.
- jastr 11y agoThis is actually not quite the reason that HT occurs before HH, and is called the Gambler's Fallacy [0]. The reason HT is likely to occur quicker is: after a failed win, HH needs two flips to win (1/4 chance), but HT can win in just one flip (1/2 chance). [0] https://en.wikipedia.org/wiki/Gambler%27s_fallacy https://en.wikipedia.org/wiki/Gambler%27s_fallacy
- jamieb007 11y agoright, so the coin toss example is not related to all the outcomes but rather just the most recent. In contrast, the OP seems to show that a prime is related to a previous prime - and that previous prime is related to a previous - so by extent, they are all related.