My name: William J. Ricciardi
Level of question: college
Who is asking: a 7th grade math teacher
I gave a matching quiz the other day and one of my students got all 9 incorrect. That got me thinking......What is the probability that someone could get all 9 questions incorrect? I teach 7th grade math and it's been a long time since my Probability and Statistics course. If possible, please explain you answer so that it might jog my memory.
This is a really interesting problem. It is sometimes called the hatcheck problem. A hatcheck has n hats that get hopelessly scrambled. The hats are returned at random. What is the probability that every person gets the wrong hat? Let's, however, stick with your situation.
where n! = nx(n-1)x(n-2)x(n-3)x...x3x2x1. A table of values helps show what happens as n increases.
As n gets large p(n) is neither very small nor very large. In fact, for n at least 6, p(n) is essentially constant. As the number of questions, n, increases p(n) approaches 1/e = 0.367879... The number e, the base for the natural logarithms, is approximately 2.71828183...