What is the probability of two people meeting in a bar for exactly 15 minutes?

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In summary, the question is asking for the probability of two people meeting in a bar for exactly 15 minutes between 12:00 and 13:00, assuming uniform arrival times. The problem has been discussed on Math Stack Exchange, where they solve it graphically and note certain restrictions, such as the arrival times being between 12:00 and 12:45. The problem may be considered ambiguous without the assumption of independent arrival times.
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Ganesh Ujwal
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Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet?I am mainly interested to see how people would model this formally. I came up with the answer 50% (wrong!) based on the assumptions that:- independent uniform arrival
- they will meet iff they actually overlap by some \(\displaystyle ϵ>0\)
- we can measure time continuouslybut my methods felt a little ad hoc to me, and I would like to learn to make it more formal.Also I'm curious whether people think the problem is formulated unambiguously. I added the assumption of independent arrival myself for instance, because I think without such an assumption the problem is not well defined.
 
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1. What is the likelihood of meeting someone in a bar?

The likelihood of meeting someone in a bar depends on a variety of factors, such as the size of the bar, the day of the week, and the time of day. Generally, bars tend to have a higher volume of people on weekends and during peak evening hours, increasing the chance of meeting someone.

2. Is it easier to meet someone in a bar than other places?

It can be easier to meet someone in a bar because it is a social setting where people are often more open and approachable. However, it ultimately depends on the individual and their personal preferences.

3. Are there certain characteristics that increase the probability of meeting someone in a bar?

Some characteristics that may increase the likelihood of meeting someone in a bar include being outgoing and confident, having good social skills, and being open to meeting new people. Additionally, being in a group or having a positive attitude can also make it easier to strike up conversations with others in a bar setting.

4. What are some potential obstacles to meeting someone in a bar?

Some potential obstacles to meeting someone in a bar may include loud music or crowded spaces, which can make it difficult to have a conversation. Other factors such as age, gender, and cultural differences may also affect the comfort level and likelihood of meeting someone in a bar.

5. How can I increase my chances of meeting someone in a bar?

To increase your chances of meeting someone in a bar, try to be open and approachable, strike up conversations with people around you, and make an effort to socialize and have a good time. It may also be helpful to go to bars that align with your interests, as this can make it easier to connect with others who share similar hobbies or passions.

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