# A ‘Chances’ Thread That Is Actually Worth Reading by Ben Jones

That's perhaps the best title I've ever come up with.

Our beloved Mollie shares a birthday with another friend of mine, and I recently discovered that they also happen to be getting married on the same day.

My comment to Mollie: “Wow, you guys are going to share not only a birthday but an anniversary! What are the chances?”

Most people who use the expression “what are the chances” in casual conversation aren’t really looking for a precise answer; they’re just trying to express that something is rare or unlikely to happen. But I work at MIT, you see – which means that on a daily basis I’m not surrounded by most people, I’m surrounded by MIT people.

This is a good thing for many, many reasons, not the least of which is emails like this:

From: Mollie Burgoon
To: Ben Jones
Date: Feb 5, 2007 8:02:55 PM EST
Subject: You know you’re an MIT grad when…

I was thinking about your question and briefly started to consider the factors I would need to put numbers to, in order to figure out the chances.

For the record:

1. I don’t think there’s too much of a bias toward births on different dates, so presumably the odds that I would have the same birthday as any random person is 1/365. (Update after way too much figuring: Actually, you’re less likely to be born in February than in other months, so given that I’m born in February, the odds are only about 0.002696 = 1/370.86 that someone will be born on my birthday, vs. an average of 0.00274 = 1/365 for the year as a whole.)

2. There’s definitely a bias toward September weddings, and a bias toward Saturday weddings, so given that we’re both getting married this year, it’s not horribly unlikely that we’d be getting married on the same day (probably not too far from 1/12 — i.e. every Saturday in June, July, and September).

3. BUT you’d have to figure that it’s unlikely that we’d be getting married in the same year — I’m significantly below the female median marriage age of 25.3. I’m not sure how to figure that one in.

So the answer is something close to 1/370.86 * 1/12ish * some factor accounting for the likelihood that we’d be getting married in the same year. (And I suppose, given that many people don’t even get married, some factor accounting for the likelihood of getting married at all.)

<3 statistics.

-Mollie

I really love this place. In part I love it because of what is here, but mostly I love it because of who is here. Of course you’ll find cool people in other places too, but enough of them to build a whole culture around this stuff?

Let’s just say the chances are slim.

;-)

### 40 responses to “A ‘Chances’ Thread That Is Actually Worth Reading”

1. Innov59 says:

;-]

2. Sh1fty says:

i did that a few times. when someone uses that phrase (not so common in croatian, but it does happen) i usually take my cell phone and calculate the chances :D regarding chances of fining enough cool people to build a whole culture like MIT’s, culture on FER(college of electronics and computer science) in zagreb is very similar. electronics and math jokes, movie nights, internal abbreviations and much more anyway, i’m pretty sure that FER isn’t the only place with a culture similar to MIT’s

3. Solomon says:

MIT really prides itself about its command over numbers.

4. Evan '10 says:

Mollie (and Ben) –
You have to keep in mind that a non-uniform distribution for weddings implies a non-uniform distribution for birthdays.

5. Sarab says:

Ah huh. Not bad. It actually is kinda interesting

6. Keri says:

I thought the same thing as Evan.

Also, I thought the same thing as Evan.

Also, <3 Mollie.

7. Keri says:

Apparently less than threes are no longer blog-friendly. Cue emo.

8. Evan '10 says:

Keri –
Try &lt;3’s.

9. Lucas says:

… Just because February is a shorter month doesn’t mean that fewer people are born on February 1 versus January 31 or August 10 or any other day of the year. The odds for that should still be 1/365 (or 4/1461 if you count leap years).

10. Matthew Kern says:

Actually, not to try to burst someone’s bubble, because I am probably wrong, but the probability found was the probability of one person randomly being born on a Feb. Date and getting married on a certain day, and in a certain year. The probability that two people are randomly born on the certain day, and are married on the same year, and married on the same day will be (1/370.86 * 1/12ish * some factor accounting for the likelihood that we’d be getting married in the same year) ^2, because both people’s events have to occur, so you multiply the probability by itself. This will be a little off, because her friend is probably more likely to get married during that year than she is, so the probability will be a wee bit higher. Given the mean, and sample size, we could approximate using the standard normal curve, but that information wasn’t given. Is it bad I like statistics this much?

-Regards
Kerndawg
P.S. I’m amazing at Pingpong.

11. Shashank says:

Freakonomics 2…maybe even better =D

12. Lucas says:

Matthew… squaring the two numbers would imply the odds of these events happening on the *particular* same day (e.g. September 8), rather than just any same day. In other words, two sixes in a row (on a die) instead of two of the same of any number back-to-back.

Of course, that assumes that the probability that one will be born AND be married equals one…

13. Laura says:

I hate statistics. But I love this story. =)

14. Elizabeth says:

Wahhhh! I want to go here so badly! But that’s ok. I will patiently *cough* wait.

15. AnonyMom says:

Ben–

The more critical question is how will you decide which wedding to attend?

16. Nan says:

What is the probability that they are marrying each other?

17. Mollie says:

Hee.

1. Keri and Evan, I tried to find the stats on the number of people born per day in the US. I had to settle for the number of people born per month, which I think is a good enough proxy for the actual probability of being born on a given day.

2. Lucas, you’re not less likely to be born in February than another month because of the number of days — it’s that fewer people are actually born per day in February. (The statistics are available on the internet.) If births were distributed randomly, you’d expect 7.6% of people to have a birthday in February, but only 7.55% of poeple are. Conversely, you’d expect 8.49% of people to be born in August, but 9.07% of people are.

3. Matthew, I assumed that I was calculating the probability of someone having all the same dates as I do. The probability of two people chosen at random having the same dates would be (all that stuff)^2, but since I’m just calculating the probability that someone would share the dates with me, it’s only to the first power (since I am sort of taking for granted that I was born Feb 4 and am getting married Sept 15, 2007).

4. I think the probability is that Ben will attend only one wedding, but both receptions.

Numbers make me happy.

18. Qiji says:

Numbers–good exercises, naturally.
What’s the chances of me eating breakfast at MIT on Septermber 1st?

19. Solomon says:

Ben please tell Mollie I am glad she is finally getting married to him. I only know them through these blogs but I can tell they really have it in for each other. Happy Wedding and Marriage and tons of little Mollies and little Adams.

20. Sabina says:

Guys, It’s urgent,
Can anybody tell me what’s the address of financial aid office of MIT, I couldn’t find it. Is it the same as the admissions address?
Also, don’t know why i can’t get into the application tracking page from my home computer, it’s weird.

21. Harish says:

Factor in the Birthday Paradox. Look it up.

22. Numbahs says:

So, I’m a physicish person, and I haven’t seen numbers in my class recently. To me, the fact that, in the words of Soloman, “MIT really prides itself about its command over numbers” is a clear indication that MIT is quite oriented toward engineering, which is partly true anyway. Just an observation….no universal point to this, but whatever.

23. Katherine says:

You don’t have to be an engineer to love math. And vice versa, I suppose. Probably should calculate that…

24. Karin says:

Except that it says that in a group of 366 people, the probability that 2 of those birthdays match is 100%. It’s slightly under 100%. They’ve forgotten about February 29th!

25. Anonymous says:

Sabina : the address is

Student Financial Services
MIT Room 11-120
77 Massachusetts Ave.
Cambridge, MA 02139
617-253-4971
617-253-9859 (fax)
[email protected]

But I can access it, I guess you should try using Mozilla Firefox, but it may doubt over the security certificate… but allow it for the current session.

26. oops, I forgot to type my name. it’s me the anonymous, and I think the address will help you. Good Luck . BTW where are you from? If that doewsn’t hurt you.

27. Vihang says:

After reading that post and the comments that follow, I’m thinking of looking up the statistics on wikipedia or something and calculate the ‘Actual Chances’.

28. Sha says:

In the spirit of cooperation, I tried to find out what the actual probability would be of the friend actually getting married that year in the first place. I looked for rate of actual weddings, since finding the percentage of unmarried people against married people wouldn’t help much, considering divorces, deaths, whatever. I guess it would be more accurate if I knew the friend’s age (Mollie’s age doesn’t count since I am taking for granted that she is getting married) but oh well.

According to NationMaster, in America the marriage rate is 9.8 marriages per 1000 people per year. However, since it takes two people to get married, doesn’t that mean that 19.6 people actually get married per 1000 per year? So the likelihood of a random person (i.e. the friend) getting married that year is 196/10000, which is simplified to 49/2500.

I hope that’s right– I would have expected it to be higher, especially since America has the highest marriage rate. But remember, this is all according to NationMaster.

Anyhow, hope that helps. By the way, this was a great blog… though it would be impossible to find the actual, accurate probability, since there are so many factors to take into account, for example the probability of there being a storm on that week and changing the weddings’ dates, or something… especially considering the theory that everything affects everything else.

And congratulations on your upcoming marriage, Mollie!

29. Christina says:

What is the probability that my mother accidentally mistook your friend for Mollie’s fiance when she first met him? Hmmmm? Because she did!

30. Ben says:

Guys, this thread derailed a bit so I cleaned it up. Let’s try to stay on topic – and not attack people!

31. Charlotte says:

Ooohhhh…..Mollie!!!!! I missed you so much. . . Try as I might, I haven’t been able to find a second blog as sincere, as inspirational, as insightful or as engaging as yours. ::Sniffles::

I hope you’re having a meaningful time at Harvard.

Hereby wishing you a belated happy birthday and an early happy wedding!

~Charlotte

32. Sabina says:

Anonymous,
I’m from Nepal but right now i’m studying in U.S. in Ohio. and what about you and thanks again

33. Great, Sabina, I am from India, and probably you know the boundary between Nepal and India is free for Indians and Nepalese.
The madman who makes people fly aka Captain SS Wandering Albatross aka Captain Interplanetary Tern aka Captain AdAstra : commander in chief of Phoenix Brigade AKA ANONYMOUS

34. Yay says:

Yay go Big Brother. Big Brother watches out for us.

35. Anonymous says:

This one falls in the most people category:

Mollie, you were born one day before my mother’s 64th or 65th birthday (I assuming that you are 22 or 23 years of age) and you are to be married on my 63rd birthday.

All the best to you young lady.

36. Dan says:

“2. Lucas, you’re not less likely to be born in February than another month because of the number of days — it’s that fewer people are actually born per day in February. (The statistics are available on the internet.) If births were distributed randomly, you’d expect 7.6% of people to have a birthday in February, but only 7.55% of poeple are. Conversely, you’d expect 8.49% of people to be born in August, but 9.07% of people are.”

I was thinking what Lucas was but now all I have to say is OHHHHHHHH I feel ya knockin’ Mollie! That makes mad sense! It’s a beyond-theory thing!

37. Young says:

Hey, Ben. As an admissions officer, what is your opinion on IvyWise and how do admissions officers treat simillar organizations from perspective students?

38. Greetings Mr. Ben Jones!

This post is not related to the topic, “A ‘Chances’ Thread That Is Actually Worth Reading,” but I would like to take this opportunity to ask you about this important matter.

I am a Class 2011 Applicant. I’ve been trying to e-mail the MIT admissions committee through its address [email protected], but a failure delivery notice bounces my mail back to me. I wanted to request the admissions committee to please consider my January SAT Reasoning Test scores in addition to my previous test results and inform the committee that I sent my latest official Transcript of Records through Speed Mail, postmarked February 5, 2007.

Thank you very much, Sir. I look forward to your reply.

39. ATTENTION : MR. BEN JONES

THE ‘CHANCES’ REPLY THAT IS ACTUALLY WORTH READING

Let us assume that once mollie’s and your friend’s wedding falls on one single day! What are you going to do??

Let me help:

I assume that Ben loves drinks. And we know Ben has to chose from two different weddings. Let us say that if he goes to one wedding, he gets ‘A’ amount of drink. Let me say that if you would have attended another wedding then either you must have got more drink, say 2A or less drink, say A/2. Both situations clearly have probability of 1/2. Now using a little mathematics, we see that if he goes to another wedding, he will get an average drink amount of :

(0.5 x A/2) + (0.5 x 2A) = 5A/4

Hmmm……thats like 25% gain! Now if you switch to the previous weding, you will again gain 25% using the same concept as you don’t know the exact amount of drinks at each wedding and the new amount will be:

(5A/4 x 0.25) + 5A/4

If you keep switching this again and again this will form a series. Lets call Nth term of it as T(n) and (N-1)th term as T(n-1), then it will be:

T(n) = T(n-1)r + T(n-1)
= T(n-1) x (r+1)

then T(n)/T(n-1) = r+1 which is greater than 1 !

this shows that this series will increase infinitely!
So, if you keep switching between the parties infinite times, the amount of drink you will get should also increase infinitely.

So you have 2 options:

1.)Switch infinite times, get infinite amount of drink
2.)Run at the speed of light and convert yourself into energy so you can be at both the weddings simultaneously

The choice is yours, best of luck!

So we see that playing with mathematics can lead us to infinite gains!

40. Mr. Ben,

I am Tanvi from Bahrain, your blogs are just awesome! They make me feel very hopeful. I am 14 and people whom I talk to other than my parents, my Mr. Blueit ( my Math teacher) and Mr. Natraj( My mentor)think it is crazy to apply at MIT at the age of 14. But this is what I want to do and this where I want to be. I don’t know what to ask you, I just want to talk to someone real cool and energetic! Next week I have my 9th grade exams and I am pretty much busy preparing but my mind every now and then wanders to dream of MIT. Must be a common phenomena with most students. I got to go. Mum needs her computer. Bye.