1) total outage is (.001)^k
2)(1-(.001^k))^365 gives you at least one connection every day of the year
3) doing 1 - (step 2) or 1-(1-(.001^k))^365 gives the probability of total outage at least once
4)plug in values of k until the number is less than .001
//Comments
for step 4, it is possible to solve the equation for k instead of plugging in values
Hamad Al Shehhi