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A partition of a positive integer n is a collection of one or more positive integers, with repetitions allowed, whose sum is n. An example of a partition of 7 is {1, 1, 2, 3}. What is the probability that a randomly selected partition of 7 contains a prime number? Express your answer as a common fraction.

 Nov 22, 2018
 #1
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Partitions of (7) =15 as follows:

 

7 = 7
6 + 1 = 7
5 + 2 = 7
5 + 1 + 1 = 7
4 + 3 = 7
4 + 2 + 1 = 7
4 + 1 + 1 + 1 = 7
3 + 3 + 1 = 7
3 + 2 + 2 = 7
3 + 2 + 1 + 1 = 7
3 + 1 + 1 + 1 + 1 = 7
2 + 2 + 2 + 1 = 7
2 + 2 + 1 + 1 + 1 = 7
2 + 1 + 1 + 1 + 1 + 1 = 7
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7

I count 12 including 7=7, which gives you: 12/15 =4/5 probability.

 Nov 22, 2018
 #2
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Nice work, Guest! I counted the ones that didn't work to get my answer. 

PartialMathematician  Nov 22, 2018

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