A couple related things happened lately. Both were promotions by companies, both used probabilities correctly, but kind of sneakily, I guess hoping that people wouldn't notice. Both are good math applications for students that are just starting out in probability and can be seen in ways they are familiar with.
First one - I was in Arby's - a place I love. They had a sign trying to get customers to go on-line to fill out a customer satisfaction survey. If so,you could "RECIEVE 10 CHANCES TO WIN $1,000 DAILY". The hook is a person figures their chances of winning has gone up tenfold. It hasn't.We don't know what are chances really are. Let's suppose they randomly chose one from eighty people that have gone on-line to take the survey. You have a one out of eighty chance of winning = 1.25%,
But wait, you have ten chances to win. So it was like you were standing in a line with seventy-nine other people. Now there are ten of you in line. But wait. There are ten of everyone else, too. Your chance of winning is not 1:80. It is 10:800. But wait. This is also 1.25%.
This technique seems to also be common in school raffles. You pay your money and they tear off three raffle tickets and hand them to you. Even if you know probability, you momentarily might think you're better off. You would be if you were the only one getting three tickets, but every entrant is getting three tickets as well. You're not getting cheated, you just aren't any better off. It's basically a marketing ploy. No harm done.
I've gone on long enough. I'll do my second example next week.
