(my possibly incorrect line of thinking in relation to this tweet... https://twitter.com/secretGeek/status/1135831731347398657 )
First thing I think is:
we're not trying to work out the probability of being caught exactly once, or exactly twice etc. So we use an old statistics trick and turn it around, asking:
What is one minus the probability that he will be caught exactly 0 times?
To set about answering this, we start by saying, how often does he drink?