Have I correctly solved the problem in probability theory?

Question

Mathematics

180 instruments are being tested at the research stand. The probability that any of these devices will fail within an hour is 0.05. Find the probability that within an hour:
a) none of the devices will fail;
b) at least one of the devices fails.
a) P(C) - an event that occurs when none of the devices fails to work.
P(C) = 1 - 0.05 = 0.95 = 95%
b) I think the answer should be 0.05 in this case, but I doubt it. What is the correct answer and how did you arrive at it?

Answer 1

You calculated the probabilities for one device (although they are already given). Given that there are many devices, the probability that one of them will fail increases.
a. (1 - 0.05)¹⁸⁰ = 0.000097
b. 1 - 0.000097 = 0.999903