Smoke Alarms

I believe smoke alarms save lives. And, in general, safety first. But last night I didn't sleep well because a smoke alarm had a low battery, and beeped every 30 seconds until I got up and pulled out the battery at 2am. I can remember 3 or 4 times this has happened to me in the past, and am wondering whether I might lead a better life without smoke alarms. Here's my analysis:
First, you have the cost of the alarm and batteries (about $50 over my lifetime).
Next, there is maybe a 1/1000 chance my home will ever catch fire (this is generous for Seattle).
Third, I'm a non-smoker, so divide that by 2.
Fourth, there is only a 1/3 chance I will be asleep at the time and need the detector to alert me of danger.
Next, let's say there is a 50/50 chance that I could have survived without the detector - maybe I had a dog to wake me up instead of the shrill beeping.
Now - the factor that I think may be overlooked sometimes - losing about 20 good nights of sleep over the course of my lifetime.
Finally, once every 2-3 years a smoke detector will tell me something I already know, i.e. I just burned some toast. That just bugs me. I guess, to be fair, I should add that there is potential comedic value in smoke detectors - you might use one in a practical joke.
So, the bottom line is you probably would win the lottery before a smoke detector saves your life. But we must put up with them to meet fire codes.