When you turn on your computer, a certain bit (0/1) is initialized to the value 0.
Suppose that starting from when the computer is turned on, the bit is incremented (adding 1 mod 2) at random times, on average λ times per millisecond. What is the probability that after milliseconds the bit stores the value 0?
I know's I'm essentially seeking the probability a Poisson process returns even number after time $t$ given λ times per millisecond, but I'm not sure how to get the answer.