### Two Good Problems

I haven't yet decided whether I'm going to use these to start the probability unit in my class. My students would be directed to use their calculators since they wouldn't know how to derive an exact answer.

- If we have a characteristic which occurs in 1 out of N people, what is the probability that in a group of N people at least one of them has the characteristic? What happens as N goes to infinity?
- Someone has randomly generated two natural numbers and used them to make a fraction. Reduce the fraction to its lowest terms. What is the probablility that both the numerator and the denominator are odd numbers?