1. Four fair coins are tossed: a) What is the probability of getting more than 2 heads? b) What are the expected winnings if you receive $1 for each head? c) What are the expected winnings if you may re-toss one coin of your choice? 2. A 20-sided die is rolled. Player A and B each choose a number before the roll. Whichever player's number is closest to the value of the die wins the amount shown on the die. What is the optimal strategy? Is it better to choose first? What are the expected winnings?