favorite probability problems

[karlson]

I have to teach a section tomorrow dealing with some basic probability. I was wondering if you guys had some favorite fun problems to share. I won't be able to use anything super complicated, just things like computing expectations, variances, using bayes theorem, using common distributions, etc. The trick is just to find a cool context. I don't feel like using gambling examples much though.

I was going through some books when I realized that this may be the best resource.

Thanks guys.