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A and B are playing a game. A randomly chooses two rational numbers between 0 and 1, both included. He keeps them hidden in two chits. B chooses any of them and guesses if the number he sees is the higher of the two. He wins if he guesses correctly. Is it possible for B to win more than half of the games that he plays with A? If yes, what is the probability?

My attempt was that the probability that B gets the higher number is higher is half , and prob that he guesses right that the given number is higher, too is half . So when the prev 2 cases overlap, he actually gets higher and guesses higher. But chances of this happening is extremely low , so i think its impossible for B to win more than half of the games.

Abhay Chandra
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    Please edit to include your efforts. And for clarity. How is $A$ choosing the numbers? Is he choosing them uniformly at random or is he specifically choosing them to mislead $B$? See this question for the random case (though they are a little vague about what uniform distribution they are talking about. The discussion works better if you have a uniform distribution on $[0,1]$.) – lulu Feb 04 '24 at 12:21

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