# Probability of arriving at office before $9$ am

I'm having trouble answering this question: A person leaves for work between $8:00$ A.M. and $8:30$ A.M. and takes between $40$ and $50$ minutes to get to his office. Let $X$ denote the time of departure and let $Y$ denote the time of travel. If we assume that these random variables are independent and uniformly distributed, find the probability that he arrives at the office before $9:00$ A.M.

Any help would be appreciated.

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## 1 Answer

Hint: Draw a square, whose base is 30 minutes in width (8 to 8:30), and whose height is 10 minutes (40 to 50 minutes). Shade red those combinations that lead to him being late, and blue those combinations that lead to him being on time. Then find the fraction of the total area that is blue.

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Nice very concrete answer! – André Nicolas Feb 21 '14 at 4:00
That actually makes a lot of sense. Should have thought of this one. Thanks! – user130398 Feb 21 '14 at 4:38
You're welcome, my pleasure. – vadim123 Feb 21 '14 at 4:39