Problem 1 (35 points). The Atlanta Falcons and the playoffs. With 5 wins and 4 l

Question

Problem 1 (35 points). The Atlanta Falcons and the playoffs. With 5 wins and 4 losses (updated it after the Sunday game with the Cowboys), meaning an up and down season, Falcons are at the moment in danger of missing the playoffs. Let's be optimistic and hope they can get into the playoffs as a wild card, which would realistically require a 10-6 record at the end of the regular season a) (10 points) Assuming that the Falcons' record so far is quite indicative of their successes probability in the remaining games, what is the probability that they finish with a record of 10-6 which will give them a good chance to win their division. b) (10 points) Since the team that is on the last wild card position, the Carolina Panthers who are at 7-3 (also updated), will not remain idle, what is the probability that the Panthers would achieve only 9 wins or less c) (10 points) Based on your results from above, are you optimistic about the Falcons chances to win 1? d) (5 points) Are there any potential concerns for the analysis conducted in parts a-c?

Explanation / Answer

Hi,
A. Currently the falcons are at 5-4, to get in via wild card they need 10-6,
now to win they need 5 more wins and at max 2 losses, going by the past trend, the probability of winning of falcons is 5/9 . now the we have to win 5 out of 7 left i.e (5/9)^5 * =0.053
B.the record of panthers is 7-3, probability of winning is 7/10,
now to only achieve 9 wins or less means, they have to lose 4 atleast, therefore probabilty is (1- 7/10)^4=0.0081
C. since the probability of B is so low, its not realstic that falcons would go through
D. the concern in this approach is that we assume the probability of win/loss of every game is independent of every other game, which might not really be the case
Thumbs up if this was helpful, otherwise let me know in comments

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