Correct me if I'm wrong, but each and every possible series of coin tosses is just as likely as any other series -- regardless of the length of the series. You cannot look at a series of "random" events that have happened and declare the series impossible or unlikely.
Correct me if I'm wrong, but each and every possible series of coin tosses is just as likely as any other series -- regardless of the length of the series. You cannot look at a series of "random" events that have happened and declare the series impossible or unlikely. You are correct with respect to any given series. For a fair coin "HHHHHHHHHH" is as likely as "HHTHTTTHTH". For distributions of results in the aggregate, however, the head-to-tail ratio should be about 1-to-1. (For a any roll of a pair of fair dice, they should total 7 about 1 out of every 6.) So based on the known properties of a coin, the probability of observing a series containing 10 heads (~.09%) is far less than the probability of observing a series containing 5 heads and 5 tails (~24.6%).