Which will be more likely to occur first
in a string of coin tosses, HTH or HTT?
This is the kind of question that becomes difficult because of assumptions made by the listener, assumptions that change the problem subtly and thus change the resulting expected probability. The listener/reader here naturally changes this question to "Which group of three is more likely?" That's not what he asked.
We should refer back to the Monty Hall question.
Source: Bob Lochel, Obvious Debate. from TEDTalk by Peter Donelly.