I have a question about how the "optimal strategy" is defined.
It seems like the strategy will depend on how "Before guessing they may toss the coin any number of times" is interpreted.
There are two alternatives, either: we specify how many times to toss the coin at the outset, observe the total number of heads, then guess whether the coin is fair or biased; or, the decision to toss again at each coin toss depends on the number of heads obtained so far.
My understanding leans towards the second alternative, but I'm not entirely sure.
Problem 852
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Don't ask for hints how to solve a problem
Don't start a new topic for a problem if there already exists one
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
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yourmaths
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brob26
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Re: Problem 852
The second interpretation is correct: the decision to toss a coin an additional time can be made dependent on the outcomes of previous tosses.