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Two A/B tests on one page - audience split question

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Hi! I've been asked to create two A/B tests to run simultaneously on the same page, both with an A/B/C 33% random split of All Visitors. 

The two tests modify different page elements with no overlap, so I'm hoping there wouldn't be any collision. (Right?)

 

But I haven't been able to find a clear answer on whether the 33% traffic split is shared between the two tests. Does test 1 create a random audience split, and test 2 create a re-randomised and different audience split? Or does everyone who sees test 1 variant A, also see test 2 variant A?

Ideally I'd like the results from the two tests to be uncontaminated by one another. 

(I considered approaching this as a multivariate test but we are not interested in how the two tested elements affect each other. We want to consider them as 2 distinct tests.)

Would really appreciate some clarification here, thank you! 

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