Question

You've just unboxed a new board game by legendary creator Stefan Feld. In the game, you roll a seven-sided, fair die with 4 red faces, 2 green faces, and 1 blue face. Your roll dictates how much gold you receive for rolling: red gives 1 gold, green gives 2 gold, and blue gives 4 gold.

a. Define a random variable for this setting, state the support, and find its probability model.

b. Find the expected value and variance of your random variable.

c. Suppose you have two special cards that can be applied after your roll. Card A triples your gold, while Card B increase the gold by 4. You will either apply Card A and then Card B, or vice versa. Write an expression using your random variable for each application strategy, and then decide which you should use by finding the expected value and standard deviation of each approach.

Answer 1