Answer Happy

3 Exercise 3. (16 points = 8 + 8) In a football game between the teams of England and Italy both teams have to take 5 penalties each to decide which team will win the trophy. The team pat scores the most penalties wins. Suppose that the probability to score a penalty is 0.65 for Italy and 0.60 for England. For simplicity we assume that they both take all the 5 penalties. All penalties can be considered independent What is the probability that Italy wins the original penalty series with 5 penalties for each team, so Italy will score more penalties than England (Round your answer to 4 decimals)? BOP a B.Op b Suppose that it is a draw after 5 penalties for each team. Both teams have to take 1 extra penalty. If there is no winner after these 2 extra penalties, both teams have to take another penatty each, to determine a winner. This process will be continued till there is a winner. What is the expected number of extra penalties till we have a winner, if we have the situation that it is a draw after the first 5 penalties for each team (Round your answer to 4 decimals)?