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 t 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) Assumingthat 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 aboutthe Falcons chances to win? d) (5 points) Are there any potential concerns for the analysis conducted in parts a-c?

Explanation / Answer

(a)

9 games have already been played by this team and only 7 more are remaining to be played.

And in order to be in the play offs, they need to win 5 out of these 7 games, the probability of which is:

P = 7C5*0.55*0.52 = 0.164

(b)

10 games have already been played by this team and only 6 more are remaining to be played.

And in order to register only 9 wins or less, they need to win either 0, 1 or 2 out of these 7 games, the probability of which is:

P = 6C0*0.50*0.56 + 6C1*0.51*0.55 + 6C2*0.52*0.54 = 0.344

(c)

Since both the above calculated probablities are well below, there is very little chance that Falcons will win.

(d)

A potential concern is that we have assumed that the probability of winning a game for both these teams is equal to 0.5

Hope this helps !

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