Here is an exercise for all you budding mathematicians out there. This event took place about a year and a half ago. I would like to think that it was an event of extremely low probability. I haven’t calculated it myself but it will be an interesting exercise for those who are interested.
I will try and give you as many details as I can. Feel free to ask me for more information that you might need to do this calculation. Here goes:
I was at home with Rupali (then my girl-friend) in Champaign when my cellphone rang. The caller ID on the phone said that the phone call was from Rupali’s brother, Tarun. So I answered the call only to hear the voice of another friend of mine, Khagendra at the other end of the line.
I looked at the phone number again and saw that the call was indeed from Tarun’s cell phone. Now, Khagendra and Tarun do not know each other. In fact, Khagendra lives in Boston and Tarun was at the time living in Philadelphia.
So obviously the first question I asked Khagendra was, “Whose phone are you calling from?” He was bewildered. “What! Why?” was his response. Well, it might have been some other form of exclamation but the point is that he was wondering why I was asking him that question.
I repeated my question and wouldn’t continue with any conversation until he told me whose phone he was calling from. He asked me to hold a minute and then shouted out to some people around him. “Hey, whose phone is this?” In the background someone said, “That’s Tarun’s phone”. This is where there was distinct jaw-dropping! Khagendra came back and said, “I don’t know why you care, but this phone belongs to some Tarun.”
Khagendra was meeting some friends in New York. It so happened that one of these friends worked in the same company as Tarun. Tarun and this guy were meeting these other friends of Khagendra’s in New York for the weekend.
Let me also add that Khagendra knows Rupali and knows her last name too. When he had borrowed Tarun’s phone to make that call to me, he had not asked Tarun his last name. If he had, he might have correlated the last name and also asked Tarun if he knew a Rupali, given that Rupali’s last name is not the most common lastname one would hear. In that scenario, this incident would not have taken place the way it did.
In any case, take on the challenge if you feel like it and help me find the probability of this event happening. You will get an honorable mention on this blog if you crack this one.
Original Question: What is the probability that amongst all the people I know personally who are my close friends, who do not know each other and live in cities geographically far, two of them meet each other in a third city and one of them happens to use the other’s phone to call me?
Updated Question [August 25, 2004][10]: What is the probability that amongst all the people who are my friends, who do not know each other and live in cities geographically far, two of them meet each other in a third city and one of them uses the other’s phone to call me?
Comments (11)
ha ha ha!!! Fantastic bro!!
Forget the probability, i’ve always hated maths! See, small world
When I was in high school I was in the school play one year. As a part of the performance one of the main characters broke a pair of sunglasses. As my mother works with an optitian (spelling?), we got some cheap sunglasses for free from him.
At one of the rehersals i removed the broken pair of sunglasses from the stage and noticed that the two lenses where unharmed (they were made of som kind of plastic). I Picked them up and put them in my pocket.
The next day I was going down the corridor in the high school. A friend of mine comes out of a classrom. He has just finished a chemistry lesson, and one of the subjects where polarized light. Being the comedian he was - and is - the first thing he asks me when he sees me is “Do you have to pieces of polarized glass by any chance?”, at first I started to deny this, but then I remembered, put my hand in my pocket and handed him the lenses I picked up the day before.
Now what are the odds of him asking about polarized glass - a silley question - and me just by chance having to pieces of polarized glass?
/Søren
The probability, surprizingly, would be quite high. Especially, coz you have to look at the probability given the fact that the circle of Indian, educated and currently in US friend circle is a very small fraction of 6 billion.
Again, you are asking the probability that a good friend calling you using cellphone of another good friend; not specific friend calling from the cellphone of another specific person.
I was speaking to Madhura the other day. She had been to Yosemite a while back. Guess whom she met there. Prof. Pandit… he was there for some conference and to give a talk in UCSB. Now what is the probability of that happening.
Something to mention on AntiAstrology blog…
How many times has a friend of yours called you from somebody else’s cellphone, someone you didn’t know. Do you remember any of those instances? Perhaps not. But would you remember this one? Most definitely yes. Especially, if someone tries to describe it to you using some “external hand” or some “supernatural phenomenon.”
BTW, main palti nahi khaa raha… I personally don’t believe in astrology.
desis in the US is a pretty small world … six degrees of separation is too exaggerated a number - you can relate to most desis (in the US) in about 2, if its far-fetched it would be 3 - ofcourse this one goes a wee bit beyond that ….
More such probabilities.
1. Mugdha’s room-mate, while she was in Minnesota is, my room-mate’s close friend.
2. A friend of mine, here in UNM, got married to some girl coming from Houston. A friend of mine, who works here in ABQ, said that one of her friend from Houston, got married and is coming to ABQ. No prizes to guess, that this friend’s friend from Houston, got married to my friend from UNM.
-SBR
Prashant - that was pretty amazing story you said. It seems that many others have faced such probabilities in their life as well.
I think this was an odd coincidence and for it to happen again is close to nothing. Only for the fact that there are so many Indians in the USA now, how is it possible that a friend will be mutual friends with your brother-in-law without him evening knowing.
BUT this could go both ways.
Great post!
Now that everyone was coming up with coincidences - the only one that I can come up with is that we both know Monty (he’s your friend, my cousin) and you and I both live in the same state - hardly hour and half from each other, and we met thru a blog.
Lastly, congrats to Rupali for her outstanding achievement! 
Niket, I’m confused. You say that the probability is quite high and then in your next comment you say that this is an improbable event because of all the other times when people have called me.
So which is it?
Aditya, I wasn’t really concerned with desis in the US. Not all my friends are desis. Besides the question as posed doesn’t imply a geographical location.
Poonam, Thanx for the congratulations! I will pass on the sentiments.
Here is some more info that might help in cracking this problem.
Total number of friends I have: 500
Now I need to think of the number of pairs that do not know each other. Dang! That is going to be tough!
Let me point out that the purpose of this post is not to imply any supernatural power controlling these events. I don’t think we need any such phenomena in explaining the world around us.
I am not sure if I need to re-word that question or not. What do you think? Is the question posed correctly?
I removed the qualifier that needed me to differentiate between close friends and just friends.
It shouldn’t have an effect on the calculation, but makes my life easier.
Something to mention on AntiAstrology blog… - Niket
Looks like you are wetting your feet for making a post on the AntiAstrology Blog. If there is interest in guest posting, Niket, feel free to register. I will set you up with an account.
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