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 The Peanuts (Posted on 2003-02-18)
Although some of the things in this problem aren't true in real life just assume they are in the question.

When growing peanuts the following happens:

• for every 2 single chambered peanuts there will be one double chambered peanut
• for every 2 double chambered peanuts there will be one triple chambered peanut
• for every 2 triple chambered peanuts there will be one quadruple chambered peanut.

When a company packages 1000 peanuts in one bag they take peanuts randomly from a giant bin that contins all the peanuts grown. What are the odds that there will be 1000 individual nuts?

•  See The Solution Submitted by Alan Rating: 3.7500 (4 votes)

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There are 1000 peanuts in a bag. So that they are all individual peanuts, single chambered peanuts have to be picked every time. The supply of the different types of peanuts is unlimited therefore the odds stay the same. Peanuts are picked individualy (ie. a quadruple chambered group has 4 chances of being picked). This takes us to 1 quadruple group (1*4=4 peanuts), 2 triple (2*3=6 peanuts), 4 double (4*2=8 peanuts) and 8 singles. 26 peanuts in all. Chances that you pick a single are then 8/26. Chances that you do this 1000 times in a row is (8/26)^1000 because the odds don't change and in order for them to be all single chambered you have to make 1000 picks. What do you guys think?
 Posted by perucho on 2003-07-27 13:56:24

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