Archive of weekly problems (week of Feb 26 - Advanced, 1st problem).

I recently was solving this problem on Brilliant: and, according to my reasoning, came to the answer of 13/16 (>0.75).

So, the strategy each one in the group of 3 people should use is the following (instead of the usual strategy presented in the solution): if a person sees 2 Heads (or 2 Tails), he says Tails (or Heads). That way 2 out of 8 all possible outcomes (cases "HHH", "TTT") at least 1 person (in these 2 cases would be everyone out of 3 people) guesses correctly.

And if a person sees Heads and Tails, he says randomly Heads or Tails (50% each) (yes, humans are not so random, but assuming that they can be, or they have a device implemented in their brains that allows them to do it). Since we have 6 out of 8 all possible outcomes (flips of coins), where 2 persons see "Heads and Tails" in each outcome (out of 8) and they say H or T randomly, and, according to the rules or conditions, at least 1 person guesses correctly with 0.75 probability chance. So we multiply (3/4)*(6/8) = 9/16.

Thus, using the strategy described above the answer then becomes 1/4 + 9/16 = 13/16.

I hope to see if someone would clarify if the reasoning is right, wrong or missing something.

Note by Fjjvchb Dbkvvj
3 weeks, 3 days ago

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