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The numbers  are written down and some of them are colored blue. A coloring is called factorific if there is at least one blue number, and for each blue number, all of its divisors are also blue.

If Grogg randomly colors some, all, or none of the numbers from 1 to 6 blue, what is the probability that his coloring is factorific?

gueesstt  Mar 18, 2018
edited by gueesstt  Mar 18, 2018
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The numbers  are written down and some of them are colored blue. A coloring is called factorific if there is at least one blue number, and for each blue number, all of its divisors are also blue.

If Grogg randomly colors some, all, or none of the numbers from 1 to 6 blue, what is the probability that his coloring is factorific?

 

I have made an assumtion here. The likelihood that any individual number is blue is 50%

 

For this to work number 1 must be blue because it is a factor of all the others.

Since 1is blue, it really doesn't matter whether 2,3 or 5 are blue as their only factor other then themselves is 1.

 

6 blue , 3blue, 2 blue, 1 blue others don't matter.   Prob = 0.5^4 = 1/16

6 not blue, 4 blue, 2 blue, 1 blue others don't matter  Prob = 1/16

6 not blue, 4 not blue, 1 blue and others don't matter  Prob = 1/8

 

1/16  +  1/16  +  1/8 = 4/16  = 1/4 

 

I think that the chance that his colouring is factoric is  1/4

Melody  Mar 18, 2018
edited by Melody  Mar 18, 2018

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