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A comment on Ask HN: We just had an actual UUID v4 collision.... Parent comment
If: p(H)p(T) = p(T)p(H)
And: p(H)p(T) + p(T)p(H) = 1
Then: p(H)p(T) = p(T)p(H) = 0.5
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If: p(H)p(T) = p(T)p(H)
And: p(H)p(T) + p(T)p(H) = 1
Then: p(H)p(T) = p(T)p(H) = 0.5