I must have missed some steps, but why did you assign p = 0.01, and how did you arrive that a) get to be (1-p) * (1-p)? And why can't, say, a) be p * p?
p is the probability of introducing in error into code.
To get some actual numbers, I choose an error rate of 1 in 100 lines of code (0.01). This is totally subjective and probably larger then in reality, but it does not hurt to be pessimistic here.
a) => the production code, nor the test code contains any bug. So if the probability for an error is `p` (.01), the probability for error free code `1 - p` (.99). If both events are independent, we can multiply them to get the probability of both happening at once `(1 - p) * (1 - p)`.
