By using recurrence

You are designing a computer for use on a long-term space travel mission. Consider the "logical" bits discussed in class. Real bits can randomly flip with a small probability p, which for this problem will we assume is p = 2 3; logical bits address the issue. A logical bit is a grouping of n bits B - (bi);_ and an operation f on those bits such that f : B - {0, 1} represents the state of the logical bit B. Suppose that Xi is the correct state of bit B; at step i of an algorithm. Define a "good" operation f and an indicator random variable E; that tells you whether Be is correct in step i, assuming it was correct in step i -1. Assume Bo is completely correct. If you do nothing other than run your algorithm on this grouping of bits, what is the probability that B, is incorrect? What about B2? Can you come up with a useful bound for the probability that, before step N - 1, B has been wrong at least once