The Design-Time Developer

What are the odds?

I went to see Mr and Mrs Smith yesterday night - it was very entertaining and a lot of the dialogue had double meaning, which I enjoyed.

However, due to the somewhat inconsistent mass transit system we know as the CTA, I had about 15 minutes to kill before the movie.  After buying my ticket, I purchase the requisite bag of Sour Patch Kids and made my way to the theater.  I was shocked to find out that we, the audience, were not even to be entertained by the trivia slides and advertisements before the movie - a bare black screen hung before me in the dimly lit theater.

Thankfully, I had a big bag of candy and my Audiovox XV6600, with an all-you-can-eat data plan.  I popped open the bag of candy and visited my favorite Internet Movie Database to find out if Mr and Mrs Smith is a remake (verdict: uncertain, although the surface theme is strikingly similar to the old Hitchcock film of the same name).  As I was surfing the web, I was simultaneously enjoying my bag of sour-flavored, sugar-coated, gummy baby things.  That is, until I observed a disturbing fact - each time I reached in to the bag, I pulled out two candies, and each time, they were the same color.  This held for three tries; the fourth was an odd pairing.  I thought to myself, "What are the odds that I would pull three pairs of matching candies in a row from a new bag of candy?"  Since I'm not particularly spiritual, instead of thinking this was an omen, I literally considered what the odds were.

   There are 4 color options in a bag of Sour Patch Kids - green, red, orange, and yellow.
   The bag identifies one serving as 16 pieces and ~3.5 servings per bag, so I'm estimating 16*3.5=56 pieces of candy.
   I'm also assuming an even distribution of colors - 56 / 4 = 14 pieces of each color
   Finally, I'm assuming that the pieces are not picked at the same time, but rather microseconds apart (which may have a slight impact on the math).

   The odds of pulling those six pieces in three color-matched pairs is therefore:
      56/56 x 13/55 x 54/54 x 13/53 x 52/52 x 13/51
   which reduces to
      1 x .2364 x 1 x .2453 x 1 x .2549 = 0.0148 or roughly 1:68

At that point, I realized that the odds weren't so bad.  It's only slightly less likely than pulling a particular card out of a full deck (1:52), which does of course assume that I'm playing with a full deck.  It's significantly more likely, however, than winning the MegaMillions Lottery Jackpot - odds of getting the big score are 1:175,711,536.  Plus, with the candy, you're guaranteed a winner every time, unless you really don't like the red ones.

Published Saturday, July 09, 2005 11:16 AM by jacobcy
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Comments

 

Steven said:

The theme of the Mr. and Mrs. Smith movie has a lot in common with the (unfortunately) short lived Mr. and Mrs. Smith TV series starring Scott Bakula and Maria Bello.

I thought I was the only one doing math puzzles while waiting for a movie to begin :)
July 9, 2005 12:47 PM
 

Steven said:

Addendum: according to the IMDB, the entry for the show lists it as being remade in the 2005 movie.
July 9, 2005 12:49 PM
 

jacobcy said:

I saw the listing for the TV show, but it didn't sound like it was supposed to be funny, unlike the Hitchcock film. Perhaps the description was not well-written, or my mind at 11:30 PM, when I was reading it, preferred to match the Pitt/Jolie movie with the Montgomery Lombard pairing vs. the Bakula/Bello pairing. Don't get me wrong, Maria Bello is one fine woman (especially in Payback), but IMHO Pitt and Jolie have an amazing stage presence that I just can't picture from Scott Bakula.
July 9, 2005 5:15 PM
 

Steven said:

The TV show was very funny. The two characters weren't married, though, and didn't try to kill each other. Why not let them explain the premise of the show?:

http://www.shdon.com/temp/smith.mpg
(on-line for a limited time only)
July 10, 2005 10:17 AM
 

jacobcy said:

Steven, I really wish you hadn't posted that. Now I want to know when the series is coming out on DVD.
July 10, 2005 12:02 PM
 

glengordon said:

Man. Cool trailer. Is it just me or is Maria Bello from that show really a knockout???
July 13, 2005 1:34 PM
 

got a D in college stats said:

the 13 in (13/55) implies that the second pair is a different color than the first pair, (otherwise it would be 11)

but

the 54 in (54/54) implies that the second pair may be the same color as the first pair.

hmmm, something's amiss here...
July 13, 2005 5:24 PM
 

jacobcy said:

Thank you, 'got a D in college stats' - perhaps I would have put up the right answer if I had taken college stats (or was not temporarily distracted by daydreams of Angelina Jolie in ill-fitting tops).

I crunched the numbers again and the outcome is even less impressive, sine I had selected three different color pairs:
56/56 x 13/55 x 42/42 x 13/41 x 28/28 x 13/27
1 x .2364 x 1 x .3171 x 1 x .4815 = .0361 or roughly 1:28

However, if I had selected three pairs of the same color, the odds are particularly more stunning (roughly 1/2500).
July 15, 2005 12:27 AM
 

The Design Time Developer What are the odds | Wood TV Stand said:

May 31, 2009 8:30 PM
 

The Design Time Developer What are the odds | alternative dating said:

June 17, 2009 3:52 AM
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