Probability of Meeting

Two men, call them X and Y, wish to meet at a certain place on a certain day, but no earlier than noon and no later than 12:15 p.m. If necessary, X will wait 6 minutes for Y to arrive, while Y will wait 9 minutes for X to arrive, but neither can stay past 12:15 p.m. Express (as a percent) their chance of meeting.

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