奇数次正面

思考这个问题的最简单方法是认识到一切都取决于最后的翻转。如果 999 次翻转后正面的数量为奇数，则需要反面。如果 999 次翻转后正面的数量为偶数，则需要正面。无论你拥有什么，$p = \boxed{\frac12}$ 都会出现所需的一面

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Original Explanation

The simplest way to think of this problem is to realize everything is contingent on the final flip. If you have an odd number of heads after 999 flips, you will need a tails. If you have an even number of heads after 999 flips, you will need a heads. Regardless of what you have, the desired side will occur with $p = \boxed{\frac12}$