Tuesday, June 15, 2010

How much of a coincidence is it? The Walt Disney World couple

Boing Boing points the coincidence of a woman spotting her husband's father and her husband as a toddler in her old family pictures that records the fact that they were at Walt Disney World at the same time as children long before they ever met and then married. The future wife is with the Mr. Smee character in the foreground and the future husband's dad is clearly visible pushing a stroller with the future husband in it in the center in the background.

It's a wonderful synchronicity that foreshadows that they were meant to be from long before they ever met, or is it? What is the probability of such an occurrence?

I think it breaks into two problems:

Problem one: Given that you were at Disney World in your youth on a particular day, and you took a picture, what is the probability that someone you know was there on the same day and in the picture.

Problem two:On the other hand, we heard about this on the news, so we could state it another way and ask, how often would we expect to hear about someone having a picture from there youth at Walt Disney World, that captured someone they know now but didn't know then in it.

Here are two comments on BoingBoing trying to figure out this probability (one, two). I think the two possibilities above are more common than you think and that the second one is very likely, I just have given up trying to formulate the problem in a clear manner since I can't quite wrap my brain around the probabilities because there are some dependent ones in here. What do you think? I have provided some data below to help:

Some data that might be helpful:

According to Park World the attendance at the Magic Kingdom was 17 million in 2007. Other estimates of milestones reached by Walt Disney World are at Disney By The Numbers. For instance the 600 millionth visitor entered on June 24, 1998. The Orlando convention and visitors bureau estimated about 3 million international visitors in 2009 (from here). Assume they all go to Disney World and are part of the 17 million total mentioned.

Kodak estimates that approximately 4 percent of all the amateur photographs taken in the United States are snapped at Walt Disney World Resort or Disneyland.

Looking at the picture itself shows about 15 people in it.

Photos printed per year (from here).

Rolls developed per year. Within the amateur market, 710 million rolls of film were developed in 1995. Total rolls were down slightly from the 1994 figure of 716 million, but higher than the 1993 total of 694. (from here). Assuming 24 photos/roll gets to 17 billion pictures, and that these are US figures, which is implied in the report.

"In fact, in 1960 newborn babies and young children were the object of 55 percent of the 2.2 billion photos taken that year." (from here)

There are over 2700 photographs taken every second around the world, adding up to well over 80 billion new images a year taken on over 3 billion rolls of film, according to estimates published by the United States Department of Commerce. (from here via there) See also this chart of the number of photos taken/year.

(via BoingBoing, via The Disney Blog, via WXII TV, photo from WXII TV)


Howard said...

Disney World opened in 1971, so I'd say it's a once in 40 years probability.

Richard said...

I agree, that, as a minimum it is a once in 40 years probability, don't flash your fancy obvious answer at me. But really, thank you, because given the data we have, that is the answer.

I was just wondering how many undiscovered pictures there are, but that is different than the question I asked. We heard of one in 40 years so that is that.