Odd of daughter meeting someone I know from middle school

Hankejp

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I need to probability help. Yesterday my daughter, who lives in Phoenix, met someone who I knew in middle school in Wisconsin. Not only that, she met this lady in a bar that had no toilet paper in the ladies room, which is what struck up the conversation. If someone can figure out the probability of this happening, that would be great. The city I grew up in is about 35,000 people.
 
Do you want this probability conditioned on whether the bar she met your schoolmate in had toilet paper in the ladies?

We're gonna need some more info about Phoenix bars....
 
I think this is one of those "Fermi questions"? - e.g.- How many piano tuner live in United States?
 
I suppose you could draw up a sort of Drake equation for it. We don't have available info for most of the terms though.
 
Do you want this probability conditioned on whether the bar she met your schoolmate in had toilet paper in the ladies?

We're gonna need some more info about Phoenix bars....
If possible I would like to include the no toilet paper. As far as bars I found this from Reddit


A quick search of the Arizona Department of Liquor website shows that over 4000 establishments in Maricopa County are licensed to serve alcohol as either a bar, reatuarant, craft brewery, or tasting room.

632 are licensed as "bars", but 2724 are licensed as "restaurants", which includes many businesses one would view as more of a bar.
 
For simplicity we'll call them all bars.

what's the probability your daughter would be found in a bar?

I suppose we can lookup the probability someone from WI travels to AZ
People from WI drink like fish so the probability someone from WI would go to a bar while on travel in AZ is almost 1.

Our Drake equation starts to look like

\(\displaystyle P_D P_{T_{WI\to AZ}} \left(\dfrac{1}{4000}\right)^2\)

\(\displaystyle P_D = \text{P[daughter goes to bar]} = ?\\
P_{T_{WI\to AZ}} = \text{P[rando person travels from WI to AZ]} = ?\\
\text{We're assuming P[rando WI traveller goes to bar] $\approx 1$]}
\)
 
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