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The numbers 1,2,3,4,5,6 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?

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MrEquation
Answer: If Gregg colored none of the numbers blue, then obviously the chance the of his coloring being factorific would be zero.

If Gregg colored all of his cards blue, then again the chance would be 100%. This is because at least one of the cards is blue and all the divisors are blue.

On the other hand if only some of the cards are blue, then are numerous possibilities for the probability. You would have to create a chart and analyze each option to make sure the divisors were also blue.

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