Question

A programmer has a 95% chance of finding a bug every time she compiles his code, and it takes her three hours to rewrite the code every time she discovers a bug. Find the probability that she will finish her program by the end of her workday. (Assume that a workday is 9 hours)

(a) 76%

(b) 44%

(c) 37%

(d) 28%

I got this question in unit test.

I'd like to ask this question from Geometric Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct answer is (d) 28%

To explain I would say: In this instance, a success is a bug-free compilation, and a failure is the discovery of a bug. The programmer needs to have 0, 1 or 2 failures, so her probability of finishing the program is: P(X=0) + P(X=1) + P(X=2) = (0.95)^0(0.1) + (0.95)^1(0.1) + (0.95)^2(0.1) = 0.28% = 28%.