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

I recently was solving this problem on Brilliant: https://brilliant.org/weekly-problems/2018-02-26/advanced/ 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.

#Combinatorics

Note by Deaf. Frust.
10 months, 4 weeks ago

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Comments

This is NOT my answer but his-https://brilliant.org/profile/mark-4vl4ha/

To win, someone has to guess correctly, and no-one can guess incorrectly. With your strategy, the team loses with HHH or TTT. In any other configuration (such as HHT) then two people (not just one) have to get their guesses right, since otherwise someone will get a guess wrong. Thus the chance of winning in such a configuration is 3/16.

saket goyal - 10 months ago
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