Prime surprise...

Prime surprise...  I ran across this interesting article about a surprising property of sequential prime numbers.  But even more interesting to me is this piece in the article, which seems obviously wrong to me:

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.

Have any of my readers ever heard of this?  Search as I might, I've found no reference to anything suggesting unequal probability of head-tail versus head-head.  At the moment I'm assuming that the article's author just misunderstood something she heard...