Last week, for pedagogical reasons, I had to solve the following problem:
In a bag there are \(4\) blue and \(5\) red balls. We randomly take \(3\) balls from the bag without replacement. Let the random variable \(X\) denote the number of blue balls we get. Find out the expectation and variance of \(X\).

A famous problem in probability is this: Suppose you randomly1 break a stick in two places. You will get three smaller pieces of stick. What is the probability that you can form a triangle using these pieces?
One interesting thing about this problem is that depending on how you visualize breaking the stick, you get different probabilities.