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combinatorics 8.24 question regarding the diagram
Hello Areteem instructors,
I recently reviewed the 8th and 9th chapters of combinatorics and rewatched the zoom video. I have a question for 8.24. the problem asks for the probability that jack and jill, given many conditions, will have dinner together. In the zoom meeting where it was reviewed + on the quiz answers, it shows this diagram:
however I noticed that the question states, Jack will wait up to 30 minutes for Jill, but will not wait at all after 5:45. This is implying that, for example, if Jack were to arrive at 5:25, that he would not wait at all past 5:45. However, the diagram shown in the quiz implies that Jack will wait after 5:45 if he arrived after 5:16. Shouldn't that mean that the diagram should look like this instead? (unless I am interpreting this incorrectly)
Thank you for taking your time to read this. Please let me know.
Your diagram did not show; if it is an image stored in a Google account, I don't think it will show up here properly. You can download onto your computer, and then upload it here.
In any case, to answer your question, let's try to find the point on the given diagram that represents the case where Jack arrived at 5:16, and Jill arrived at 5:46. By the description of the question, Jack waited till 5:45 and then left, so they didn't meet. In the diagram, each point represents the arrival times of these two people. The coordinate corresponding to Jack's arrival time is the $y$ direction at $16/60$, and for Jill's arrival time it is the $x$ direction at $46/60$. This point is outside the shaded region.
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