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I think that a solution for 21 is ( R | R ) & ( R | R | R ), but the method I used is not directly extensible to the other two cases.

Let's say that En is an expression formed or'ing and and'ing R's together, and let's call P(En) the probability that a bit is 1. So P(R)=1/2; P(R|R)=3/4 and so on. So we find that:

P(E1 & E2) = P(E1)*P(E2)
P(E1 | E2) = P(E1)+P(E2)-P(E1)*P(E2)

So if you want P(Ex)=21/32 it's easy, because 21/32=7/8*3/4 and I know (from your list) that P(R|R|R)=28/32=7/8 P(R|R)=24/32=3/4.

But it's not applicable to 23/32 (23 being prime) nor to 27/32 for you can'e decompose this fraction in the product of integer fractions of value<1.

Rule One: "Do not act incautiously when confronting a little bald wrinkly smiling man."

In reply to Re: Boolean math: Fill in the blanks. by psini
in thread Boolean math: Fill in the blanks. by BrowserUk

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