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Jane Street Interview Question

Jane StreetQuantitative Researcher Interview

Robot wakes up every morning and does one of the following things with equal (1/4) probability: 1) self-destroys; 2) does nothing; 3) clones himself (so you have 2 robots); 4) clones himself two times (so you have 3 robots). If you have one robot at the start of the first day, what is the probability that, eventually, you will have no robots?

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