I’m stuck on this particular stats question and I’m not sure how to go at it.
“In a nuclear reactor, the time between occurrences of the core overheating is known to have an exponential distribution, with the average time between occurrences being 14.7 weeks.
Suppose we examine three of these nuclear reactors, which function independently. What is the probability that exactly one of the three reactors will have an occurrence of the core overheating within the first 5 weeks?”
Thanks in advance!
HINT
This is just coin flips. The probability of one of them overheating within 5 weeks is $1-e^{-5/14.7}.$ So what's the probability of exactly one coin flip out of three being 'heads' if the probability of heads is $1-e^{-5/14.7}?$