Discrete Mathematics
# Discrete Probability Distributions

Jill has a set of $33$ cards labelled with integers from 1 through $33.$ She faces all the cards down, shuffles the deck repeatedly and then picks the card on the top. What is the probability that the card she picks shows a number larger than $19?$

**Note:** No two cards have the same number.

Harry spins a roulette which consists of integers from 1 through $14$ (not necessarily in order). What is the variance of the outcome he gets?

**Note:** The areas that correspond to each number are equal.

What is the expected value of the outcome when throwing a fair die?