At the grocery store, the total for my purchases came to an even $60. The cashier looked at the number and said, "Wow, right on an even ten dollar amount. What are the odds?" I replied, "999 to 1 against."
She gave me a quizzical look and said, "What?" I explained, "There are 1000 different amounts in a ten dollar range, of which only one results in an even ten dollar amount. So the probability of that occurring are one out of a thousand, or 999 to 1 against."
I didn't get a high score on my English SAT, and so I'm not quite sure what word best describes the look she gave me!
But of course, probability is inherently confusing. I'm 85% certain that 78% of the 31% of students who take probability only understand 43% of it ... more or less that is.
Mathematics has a terrible reputation for being both difficult and boring. This is almost certainly the result of curricula that have little to do with the day-to-day calculations we find ourselves making.
For example, how can we expect students to take Probability seriously when we teach them that flipping a coin gives us "even odds"? When is the last time you needed to factor a quadratic or graph a cubic? Why aren't Geometry students excited to learn how to calculate the surface area of a cone? And seriously, how can anyone expect to have a happy marriage without using natural logarithms every day?
A classic problem in Algebra goes as follows: If a hen and a half lay an egg and a half in a day and a half, how many eggs do six hens lay in seven days? Only a mathematician would question the egg-laying attributes of fractional hens.
Don't get me wrong. I love mathematics! I'm a State Certified Math Nerd who back in High School had memorized pi out 314 places. But even my love of mathematics doesn't blind me to the insanity of how mathematics is used (and abused and confused) in the real world. It's no surprise that young people have trouble understanding financial math when you ask them what's the square root of 25% and they say it's 5%. Umm ... you do know it's 50%, right?
My favorite example of probabilistic wagers we make without truly thinking it through is life insurance. When you buy life insurance, you're betting that you're going to die and the company is betting that you're going to live. The irony of this bet is that you make the bet hoping that you lose it!