Random Probability Question

Hello!

Sorry if this is not the right forum for this, but I am having trouble finding a spot where I can ask my question. I have a probability question that I just need an answer for. This is for my own knowledge, I do not need this information for an exam or anything. I understand if this does not get answered because of this.

Background: My boss lives in the US and we have a business partner that lives in Greece. They both went on vacation this week, but did not tell each other when they were going to take vacation or where they were going to vacation. Both my boss and international partner ended up traveling to the Cairo and are staying at hotels that are across the Nile from each other.

Question: What is the probability that my boss and our international partner:

1. Would end up in the same city?
2. Would end up in hotels across from each other in the same city?

All without previous knowledge of each other traveling.

Thank you so much!

 

1. The probability that both your boss and the international partner end up in the same city can be calculated by considering the probability of each independently going to Cairo. Let's assume there's a 50% chance your boss goes to Cairo and a 50% chance the international partner goes to Cairo (these are hypothetical probabilities). The probability of both events happening (your boss going to Cairo and the international partner going to Cairo) is the product of their individual probabilities: 0.5×0.5=0.250.5×0.5=0.25 or 25%.
   
   
2. The probability that they end up in hotels across from each other in the same city depends on the layout of the city, the number of hotels, and the specific locations of the hotels they choose. Without further information, it's challenging to provide a precise probability. However, assuming all hotels in Cairo are equally likely to be chosen and they have an equal chance of choosing hotels across from each other, you could estimate the probability as the reciprocal of the total number of hotels in Cairo. If there are 100 hotels, for instance, the probability would be 1/100=0.011/100=0.01 or 1%. Keep in mind, this is a simplified estimation and actual probabilities may vary based on real-world factors.
   
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