@Jayne – Yes, there was a typo. Sorry about that. Of course it’s 1—(364/365)^365 (let’s not consider the issue of leap years).
It’s actually a real story which happened when my kids were about 15. After church they asked me, “Isn’t it weird that it’s no one’s birthday today? The church was packed with almost 400 people.” I replied that my guess is there’s one chance in three something like that happens.” “No way, Dad.” “Let’s get our pocket calculator. Or let’s just use Google.” “Google doesn’t know things like that.” “I’ll show you.” and we typed (364/365)^365 into the search field. They were not aware that Google was a calculator. Normally they know more about the web than I do. The result surprised them.
It’s my opinion that real life problems like this is what gets kids interested in math. Otherwise it’s just a set of boring formulas on black boards.
We need to share our favorite math problems with kids and get them interested in science and technology.
Here’s another one: You’ve got a toy cannon shooting balls across the room. When the cannon is on the floor 45 degrees is the optimal angle to shoot as far as possible (we ignore air, wind etc.
Now you got a table which is h cm high. Tell me the optimal angle depending on h. It’s obvious that the angle gets smaller the larger h gets. But what is it exactly? I remember discussion this in physics class in 11th grade.