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This was a bit tricky! I wasted some time trying to solve it in terms of probabilities when the simpler approach is to simply think about expected values. Remember, the expected wait time for an event is the reciprocal of its probability: if something has a 1/3 chance of occuring each second, you can expect to wait 3 seconds for it to happen. Sounds kind of obvious but maybe it will help someone.
Makes total sense, thanks, this clarified it.