# Math

How do you solve:

n is 2 given that it is even

The directions say "let n be a randomly selected integer from 1-20. Find the indicated probability"

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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1. 1. Since the coin toss can go either way with 50% probability, before tossing coin, the chance of the player mentioned winning is 51%

2. The question overlooks the new rules that require overtime to be played in the event of a tie at the end of four periods.

a. wins: 0%
loses: 1 - 0.99^2 = 0.0199
ties: 0.99^2 = 0.9801

b. wins: 0.45^2 = 0.2025
loses: (0.55)^2 = 0.3025
ties: 2*0.45*0.55 = 0.4950

c. Try 2 point conversion first, then try it again only if the first attempt fails.
2 and then kick for 1 (a win): 0.4455
2 and then kick for 0 (a tie): 0.0045
0 and then 2 (a tie): 0.2475
0 and then run/pass for 0 (a loss) 0.3025

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