Problem 2 [21 points (3, 3, 3, 3, 3, 6)]: Build-anomial When soccer matches end in a draw they may be decided by a penalty kick shootout. Team A and team B each take 5 shots at the other goal and the team with the most goals, of the 5 opportunities, is the winner. Assume that 60% of these shots are successful, each independent of all the others. i. What is the probability that team A makes 5 penalty kicks? ii. What is the probability that team A makes no penalty kicks? iii. What is the probability that team A makes their rst 3 kicks and misses the last 2? iv. What is the probability that team A makes exactly 3 penalty kicks, in any order? v. What is the probability that team A makes at least 4 penalty kicks, in any order? vi. What is the probability that after 2 shots both teams have the same total number of goals