I like Jared Diamond's column about the risk of dying from slipping while showering. (link) He's talking about repeated taking of small risks. He also differentiates between risk you can control, and risk you can't. He gives fodder to those who won't walk out of their building fearing the falling air conditioner.
I just want to point your attention to one of his minor sentences: "Life expectancy for a healthy American man of my age is about 90. (That’s not to be confused with American male life expectancy at birth, only about 78.)"
He is 75. The average American life expectancy is 78. Is he delusional to think he has 15 more years to live rather than three more years?
Here's where a bit of statistical reasoning helps. Because he has already lived to 75, his life expectancy ought to be above the American average. The fact that he is a healthy 75-year-old gives us useful information--the information that he is probably one of those Americans who live longer than most. If you want to do the math, you should restrict your sample to only those people who have lived to 75, and then compute the distribution of their remaining life. That gets Diamond to his estimate of 15 more years.