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... and the ##\mathbb{F}_8-##basis over ##\mathbb{F}_2## with its multiplication rules.
I find #6 ambiguous. If an urn has 3 whites and 1 black what do you think is the probability of drawing 3 that are either all white or all black?StoneTemplePython said:Problem 6 is still open.
The only way I can make a reasonable problem from the way it was posed is as follows:StoneTemplePython said:Problem 6 is still open.
I'd be much obliged if someone tackles it
Zafa Pi said:The only way I can make a reasonable problem from the way it was posed is as follows:
The probability of getting all white or all black from urn 2 is prob all white + prob all black.
In that case it is impossible due to Fermat's Theorem and n ≥ 3.
That's what Fermat told me.
1/43 + (3/4)3. We draw with replacement.Zafa Pi said:If an urn has 3 whites and 1 black what do you think is the probability of drawing 3 that are either all white or all black?
Huh?Zafa Pi said:In that case it is impossible due to Fermat's Theorem and n ≥ 3.
Let N be the number of balls in each urn, W the number of white balls in urn 1, b and w the number of black and white balls in urn 2, n > 2 the number drawn from each urn. With my interpretation in #73 of the problem we get:mfb said:Huh?
I think that the way the problem was formulated is problematic. I attempted to point that out to @StoneTemplePython in post #72, but received no response.mfb said:Ah. I interpreted "the probability that all white balls are drawn from the first urn" as probability that every white ball in the urn is drawn at least once.
Zafa Pi said:I think that the way the problem was formulated is problematic. I attempted to point that out to @StoneTemplePython in post #72, but received no response.
For example, If an urn contains 3 whites and one black, then what is the probability of drawing (with replacement) three balls such that they are either all white or all black? I think the only reasonable answer is ¾3, which = the probability of drawing three white balls. Thus urn 1 and urn 2 are the same is a solution.
Perhaps it should be said that the urns contain at least 3 (or n) of each color.
Zafa Pi said:That's what Fermat told me.
This is actually the easiest part of all. Let's say we have the minimal polynomial ##x^3+x+1=0\,##, and we assume a root ##\xi \,##, i.e. an element which satisfies ##\xi^3+\xi +1 =0##. ThenQuantumQuest said:From there determine a basis of ##\mathbb{F}_8## over ##\mathbb{F}_2## and write down its multiplication and addition laws.