Is it possible for a Senju to awaken a Rinnegan? Suppose that a Senju got an EMS from an Uchiha and implanted it, would he also awaken the Rinnegan just like an Uchiha did, given that the ratio of Uchiha and Senju DNA is different than if an Uchiha awakens it?
Answer given by @Ero Sɘnnin in the comments.
Not every Uchiha is able to awaken the Rinnegan. Nor can any common Senju.
It is not the Uchiha:Senju DNA ratio that governs the Rinnegan's existence. It is the Asura and Indra chakra mixing.
Also, I think the chakra ratio doesn't matter as we see in Madara's case. Although more chakra can maybe speedup the process of Rinnegan formation.