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Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between $1$ p.m. and $2$ p.m. Both of them will arrive independently at random times within the hour. Adam is greatly interested in the meeting, therefore he is willing to wait for Eve even up to half an hour, while Eve is willing to wait for Adam for $10$ minutes. What is the probability that they will meet during that hour?