Discrete Mathematics
# Expected Value

$3.5.$ If you roll 5 six-sided dice, what is the expected value for the sum of the numbers rolled?

If you roll a six-sided die, the expected value for the number rolled is$S$ and the ace of hearts is card number $H$, what is the expected value of $S+H?$

A standard deck of 52 cards is shuffled randomly, and then the cards are flipped over one-by-one. If the ace of spades is card numberSix friends are doing a "secret santa gift exchange". Their names are placed into a hat, and each person chooses a name randomly (without replacement) from the hat.

However, this leads to the possibility that someone chooses their own name and doesn’t get a gift! What is the expected value for the number of people who will choose their own name?

$\frac{3}{4}$ and 1 unit to the left with probability $\frac{1}{4}$. What is the expected value for Andy’s location after one hour?

Andy the Ant is on a number line at the location 0. Each minute, he travels 1 unit to the right with probability