A prime time game
Adam and Zoe have a deck of 99 cards, numbered from 1 to 99. Adam picks a card at random without looking, and then Zoe does the same.
When they both reveal the cards they picked, if the greater common divisor of the numbers on the cards is 1 (i.e they are coprime), Zoe wins. Otherwise it is Adam.
What is the probability that Adam wins the game ?
The answer is 0.380952381.
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