1. A tennis player wins a math 55% of the time when she serves first and 47% of the time when her opponent serves first. The player who serves first is determined by a coin toss before the match. What is the probability that the player wins a given match.
2.A football team is losing by 14 points near the end of a game. The team scroes two touchdowns (worth 6 pts each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick(which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time).
a.If the team goes for 1 point after each touchdown, what is the probability that the coach's team wins? loses? ties?
b. If the team goes for 2 points after each touchdown,what is the probability that the coach's team wins? loses? ties?
c. Can you develop a strategy so that the coach's team has a probability of winning the game that is greater than the probability of losing? If so, explain your strategy and calculate the probabilities of winning and losing using your strategy.
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