OK here's the problem, I have 1000 Network switches in a network. The switches are all rated as 1 failure in 300,000 hours.

After how many hours should I expect 1 of them to fail?

The other people here are saying 300 hours but I do not think that it is as simple as 300,000 / 1000.

This calculation does not seem right to me as it assumes that all the switches are mutually dependent as far as MTBF is concerned.

I'm saying 1500 hours for a 99.3% chance that at least 1 switch has failed.