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.

dgfgrafgdfge111
Nov 22, 2018

#1**+3 **

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.

Guest Nov 22, 2018

#2**+3 **

Nice work, Guest! I counted the ones that didn't work to get my answer.

PartialMathematician
Nov 22, 2018