SHOW YOUR THINKING ON SEPARATE PAPER' THE MORE STEPS YOU SHOW, THE MORE PARTIAL CREDIT I CAN GIVE YOU. 1. (7 pts) Draymond Green, a basketball player with the Golden State Warriors, is a 70% free throw shooter. This means that the probability that he makes the basket on any given free throw is 0.7. Now he takes three free throws and we will assume free throw successes are independent. What is the probability he will make all three shots? 2. (7 pts) 10% of prisoners in a Canadian prison are HIV positive, A test will correctly detect HIV 95% of the time, but will incorrectly \"detect" HIV in non-infected prisoners 15% of the time (false positive). If a randomly selected prisoner tests positive, find the probability the prisoner is HIV+. 3. (8 pts) At the county fair, a booth has a coin flipping game. You pay $2.50 to flip two fair coins. If the result contains one or two heads, you win 33. If the result is two tails then there is no prize. Find the expected net win (or loss) for the player in this game' Find the expected total net gain or loss for someone who plays this game 50 times. ZOOM +