12-13-2008, 01:55 PM
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#7 (permalink)
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Junkie
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Quote:
Originally Posted by twistedmosaic
Easy question: What is the probability that if you gathered 16 packs from a large population, you would have one of each combination?
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Spoiler:
The odds of getting any one of the individual packs in a single pick is 1/16. To verify this look at probability of a the color of a single candy being color a) which is 1 in 4. Then look at the probability of the color of the second candy which is also 1/4 (though technically it is slightly smaller since the population has been lowered by the first pick, I'm assuming the population is essentially infinite and an earlier pick doesn't affect the probability of a future event, thus each pick is an independent event). Multiply them together and you get 1/16.
Now we just have to compute the successive probabilities. The first pick has perfect odds (16/16) of being unique. The second pick has the odds of 15/16 of being unique and so on and each successive pick is 1 less on the numerator. Thus your odds are 16!/16^16 is equal to 1 in 881,657.952.
I would try to simplify my expression but i don't have a pen and paper to do it and typing it on a computer would be a pain so you will have to live with the decimal representation.
I'll leave the middle one for someone else thought if you follow the way I did this one and the hardest one it shouldn't be to hard.
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