3. Your computer science friend has written a new app that allows users to pay a fee to win a prize. Here's how it works: Each time the user wants to play, they must pay k pennies (where k is an integer). Then, the user will either win $4 (with probability g), $16 (with probability 3%), $64 (with probability ), $256 (with probability ), etc. a. Show that the probabilities in this problem sum to 1, as they must. b. What value should your friend choose for k if the goal is to keep the fee as low as possible, but for the programmer to make money on average? [WISE]