Your favorite college football team has had a good season so far but they need to win at least two of their last four games to qualify for a New Year’s Day bowl bid. Oddsmakers estimate the team’s probabilities of winning each of their last four games to be 0.60, 0.50, 0.40, and 0.70, respectively. 

(a) What are the chances that you will get to watch your team play on Jan. 1? 

(b) Is the probability that your team wins all four games given that they have won at least three games equal to the probability that they win the fourth game? Explain. 

(c) Is the probability that your team wins all four games given that they won the first three games equal to the probability that they win the fourth game?