Probability of 3 Events Occurring.

NoAbyss

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May 3, 2016
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Hi, I'm struggling to get my brain around this which isn't a surprise if I'm honest. I have tried reading up on probability but cannot seem to win so I was hoping someone here could maybe help please?

I was ill for 5 years and housebound. Other than going to the hospital the only time I left the house was when my brother was going to collect some stuff he had bought on the internet. I'm better now and I started talking to a girl that I met on a dating site who is Polish but lives in my city now. I've been getting told by a tutor for ages that I should visit a particular city in Poland for ages and when I told her this it transpires that it's where she comes from. After getting to know each other a little better I recounted to her the story of me being unwell and going with my brother to pick up those chairs the one time I actually left the house and when I told her where it was it was the street she lived in at the time. We have a joke that it must have been fate that brought us together, but I think it would be interesting to know the odds of us actually meeting sharing these 3 coincidences. There's roughly 7000 streets in my city so that's 1 in 7000 chance in it being her street, there's 1,200,000 people in the city so that's a 1 in 1.2m chance of meeting her and there's 8853 villages, towns and cities in Poland so that's a 1 in 8853 (at a stretch) chance of me saying where she was from. What are the odds of us meeting given those variables?
 
Well, real life is a fair bit more complicated than a statistics exercise, but essentially what you've done here is a process known as Fermi Estimation, which is good enough for a good approximate. However, I can think of one oversight. You mention that you met the girl in question on an online dating site. Hence, the odds of meeting that particular person are not simply a matter of considering the population of your city, but you must account for the number of women from your area on that specific dating site (you can potentially further narrow the scope by limiting to a specific age range or accounting for other known variables, such as her being from Poland). Once you have all that data, you can calculate the probability of all three conditions being met.

As a hint for how to approach this, consider a standard deck of cards. If you shuffle the deck and draw the top card, you have a 1 in 13 (4 out of 52) chance of drawing a Jack, and a 1 in 4 (13 out of 52) chance of drawing a Spade. What, then, is the odds of drawing the Jack of Spades? You can use known facts about a standard deck of cards to help you out, if needed. Now, can you see how to apply this information to your problem?
 
Hi, I'm struggling to get my brain around this which isn't a surprise if I'm honest. I have tried reading up on probability but cannot seem to win so I was hoping someone here could maybe help please?

I was ill for 5 years and housebound. Other than going to the hospital the only time I left the house was when my brother was going to collect some stuff he had bought on the internet. I'm better now and I started talking to a girl that I met on a dating site who is Polish but lives in my city now. I've been getting told by a tutor for ages that I should visit a particular city in Poland for ages and when I told her this it transpires that it's where she comes from. After getting to know each other a little better I recounted to her the story of me being unwell and going with my brother to pick up those chairs the one time I actually left the house and when I told her where it was it was the street she lived in at the time. We have a joke that it must have been fate that brought us together, but I think it would be interesting to know the odds of us actually meeting sharing these 3 coincidences. There's roughly 7000 streets in my city so that's 1 in 7000 chance in it being her street, there's 1,200,000 people in the city so that's a 1 in 1.2m chance of meeting her and there's 8853 villages, towns and cities in Poland so that's a 1 in 8853 (at a stretch) chance of me saying where she was from. What are the odds of us meeting given those variables?
There are lots of trouble with this problems. Suppose for example there are 7000 streets in your city and 6999 of these streets have a high concentration of poor people. One street has people with lots of money. Now if the cost of the dating site is restrictive to most people in the 6999 streets than it could be a 50% chance that someone randomly chosen from the dating service comes from the rich street, not 1/7000! What do you think others problems might be?
 
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