Candy Distribution

A bar graph of the colour distribution in a recently opened extra-large packet of Smarties. Like most people, I have an intrinsic (false) expectation that random distributions will result in relatively even numbers of each colour, and that the difference in purple and brown is meaningful in some way. But in a truly random system any variation (including one where purple leads by a large margin) is equally likely.

I have yet to open a box that’s all red. 🙂 What a glorious day that would be. Assuming every box has 71 Smarties in it, the odds of getting a completely solid box of one colour are 1 in 23,446,881,315. (if my math is right : (71+(8-1))! / (8! x 71-1!)  )

(Edit: An update on the math here. The formula I used tells you the number of possible combinations of 71 smarties in 8 colours, but with some combinations being more likely than others, it doesn’t correlate directly to the odds. ie: There’s one set where all of the smarties are green, but 71 sets with 70 green and 1 red. As Fred points out, the actual odds are probably closer to 8^71, but it gets a bit more complicated when the order doesn’t matter – I’ll have to consult my stats books. 🙂 )

Of course, a box of all reds is likely to trip some kind of Oompa-Loompa alarm at the Wonka factory, and they’ll toss me into a vat of chocolate and sing a catchy song while I’m being candy shelled.


3 thoughts on “Candy Distribution

  1. I’m also bad at math but that number seems low. It might also be the wording but I think there’s a distinction between odds and probability.

    I think probability is like “1 in 50” whereas odds are like “1 to 50”.

    I think the probability of getting a box full of the same color is “1 in 8^70”

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