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Problem 727

Posted: Tue Nov 03, 2020 4:28 am
by yourmaths
I have assumed that "chosen uniformly" means that all combinations (ra, rb, rc) within the defined limits has an equal chance of being chosen. Is this right or does "chosen uniformly" mean something different here?

Re: Problem 727

Posted: Tue Nov 03, 2020 6:35 am
by MuthuVeerappanR
Hi yourmaths,
"chosen uniformly" here means we choose one triple from among those which satisfy the limits AND the GCD condition.

If you consider only the limit, you'll have a total of $\displaystyle \binom{100}{3}$ triples to choose from. But we will have lower number of triples because of the GCD condition.

Re: Problem 727

Posted: Wed Nov 04, 2020 1:22 am
by yourmaths
Thanks MuthuVeerappanR.
That is as I understood it: each valid combination is counted once in the expected value calculation.