One of the things we do when we go out of town for an extended period of time is to double lock all our doors, etc. Usually if we’re out for the day - to work, for instance - we don’t bother doing this. Is this irrational?
Yes: If the probability of being burgled is an iid process.
But should I be thinking conditional probability? If the probability of being burgled depends on whether the burglar thinks the house is empty then perhaps this is rational behavior, since the probability that the house is empty is larger when we're away?