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f666

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In summary, 30% of students came into a coffee shop for Dan's office hours, 20% of them got hot chocolate, and 50% got nothing. Out of the larger group of people in the shop, 65% got coffee, 10% got hot chocolate, and 25% got nothing. Based on this information, the chances of someone in the shop being a student who came for office hours and got hot chocolate is 1/3 or 33.33%. This is calculated using Bayes Theorem and taking into account the total number of people who got hot chocolate (120) and the number of those who were students (40).

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f666

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- #2

HOI

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Imagine 1000 people in the coffee shop. 20% of them, 200, are "students coming for Dan's office hours" and the other 80%, 800, are not.

Of the 200 'students coming for Dan's office hours", 20%, 0.2(200)= 40 students, got hot chocolate, 50%, 0.5(200)= 100 students, got nothing, and I presume that the remaining 60 students got coffee.

Of the 800 people what are NOT "students coming from Dan's office hours", 65%, 0.65(800)= 520 people, got coffee, 10%, 0.10(800)= 80 people, got hot chocolate, and 25%, 0.25(800)= 200 people, got nothing. (That adds to 800 people so our assumption that "coffee", "hot chocolate", or "nothing" are the only options is valid.)

"What are the chances that someone in the shop during those two hours was a student who came in for office hours given that they got hot chocolate?"

From above, a total of 40+ 80= 120 people got hot chocolate. 40 of those were "a student who came in for officice hours" so the probability that "someone in the shop during those two hours was a student who came in for office hours given that they got hot chocolate" is 40/120= 1/3.

- #3

f666

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Yeah the wording is confusing unfortunately, I didn't make up this problem. Yes, the larger group is assumed to be non-students (general public). This problem involves Bayes Theorem but I am having trouble with plugging in the numbers

The chances of a student getting hot chocolate at Dan's office hours depend on various factors such as the availability of hot chocolate, the number of students present, and Dan's personal preference. Generally, if hot chocolate is available and there are not too many students, the chances are high.

No, hot chocolate may not always be available at Dan's office hours. It depends on whether Dan has prepared hot chocolate or if there is any left from a previous event. It is always a good idea to check with Dan beforehand or bring your own hot chocolate if you want to be sure.

No, there are no specific requirements for a student to get hot chocolate at Dan's office hours. However, it is expected that students attend the office hours for academic purposes and not just for the hot chocolate.

Yes, a student can request hot chocolate at any time during Dan's office hours. However, if there are many students present, it may take some time for Dan to prepare the hot chocolate. It is best to ask for it at the beginning of the office hours.

The frequency of hot chocolate being offered at Dan's office hours may vary. It depends on Dan's schedule and availability to prepare hot chocolate. However, it is safe to say that it is offered at least once a week or more frequently during colder months.

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