Physics is intimately bound up with probability and statistics for two main reasons. First, both thermodynamics and quantum mechanics are intrinsically probabilistic theories. So are some others, but those two in particular really embody the statistical concepts central to modern physics. Second, much of experimental physics is done at the bleeding edge of what our instruments can measure. It’s rare that a single measurement can adequately test a theory. Generally one has to conduct the same experiment numerous times to be sure whether an observed effect is real or just noise. This is especially true in experimental high-energy physics because by definition the effects you’re most interested in occur at the very top of the energy range available in your collider. As such, physicists spend a lot of time thinking about chance and statistics, and how those concepts affect the validity of their results. Scientists aren’t the only ones who think about chance, of course. How often have you heard the following?
“The lottery is a tax on those who don’t understand probability.”
I hear it all the time, and I used to say it. It’s partially true: most people don’t understand probability. Ignorance of the mathematical theory completely aside, most people have had their intuitive grasp of chance completely wrecked by the gambler’s fallacy and confirmation bias. The mathematical problem of the lottery is something like this.
Over the very long term, on average you expect that you’ll end up with per-ticket winnings of (lottery prize)*(odds of winning that prize). As an example, the multi-state Mega Millions lottery costs a dollar to play and the odds of winning are about 1 in 175 million. If you win, the prize varies depending on various obscure factors but the current value as of this writing is 43 million dollars. So for every dollar you spend, you can expect to win about 24 cents. Of course the vast majority of the time you fail to win the jackpot and you get nothing, and very rarely you’ll win millions of times the ticket cost. There’s smaller prizes too, so in reality the 24 cents is a low estimate. I haven’t done the math, but according to the lottery site the average payouts are roughly 50 cents on the dollar counting the smaller prizes. Still very much against you - much worse than most casino games.
But even if you win the lottery, if you play long enough you’ll lose your winnings. That’s why it’s called the tax on people who don’t understand probability.
On the other hand, insurance works the same way. On average, you’ll pay more into your homeowner’s insurance than you expect to get back from your house burning down - because (hopefully!) your house probably won’t burn down and thus you’ll never see any money back. Over the long term, you lose just as surely as with the lottery.
The reason people buy lottery tickets and fire insurance is that there’s more to the expected value than the money. The damage to one’s livlihood caused by losing a home without insurance is much more severe than just the dollar amount, and so people quite wisely purchase insurance. Lottery tickets aren’t exactly a necessity, but if people understand the odds and still pay the dollar for the fun of the wager that’s not irrational either.
Not that I’m encouraging you to gamble! I don’t gamble myself, and it’s a poor financial decision which can result in addiction with some people. Strictly on the math however, I no longer think it’s a tax on ignorance.