Consider the following game. The game uses a deck that contains 100 cards numbered 1 to 100. The deck is shuffled and cards are dealt one at a time until you choose to stop dealing. If you choose to stop dealing after exactly n cards are dealt and if the cards were drawn in ascending order, then you win $201 1). For example if you stop after three draws and the cards showing are 3,172? you win $4 but if they are 3, 27, 17 then you win $0. (a) [3 points] Find the probability that the first 5 cards drawn are all below 50. (b) [4 points] Suppose your rule is to always draw exactly n = 2 cards. What is the probability that you will win exactly $2(n 1)? Repeat for n = 3, 4, 5. (c) [3 points] Assuming that the first card drawn was 47, and your rule is to always draw 5 cards (that is 4 more cards), what is the probability that you will win $8? (d) [3 points] Can you think of a strategy that tells you whether to continue drawing cards based on the value of the last card drawn? Describe your strategy