Which NCAA college basketball conference has the higher probability of having a

Question

Which NCAA college basketball conference has the higher probability of having a team play in a college basketball's national championship game? Over the last 20 years, the Atlantic Coast Conference (ACC) ranks first by having a team in the championship game 10 times. The Southeastern Conference (SEC) ranks second by having a team in the championship game 8 times. However, both conferences have had teams in the championship game only one time, when Arkansas (SEC) beat Duke (ACC) 76–70 in 1994 (NCAA website, April 2009). Use these data to estimate the following probabilities.

a. What is the probability the ACC will have a team in the championship game (to 2 decimals)?

b. What is the probability the SEC will have team in the championship game (to 2 decimals)?

c. What is the probability the ACC and SEC will both have teams in the championship game (to 2 decimals)?

d. What is the probability at least one team from these two conferences will be in the championship game? That is, what is the probability a team from the ACC or SEC will play in the championship game (to 2 decimals)?

e. What is the probability that the championship game will not have a team from either of these two conferences (to 2 decimals)?

Explanation / Answer

A) P(ACC will have a team in championsip game) = 10/20= 0.50

B) P(SEC will have a team in chamiponship game) = 8/20 = 0.40

C) P(both SEC and ACC having a team in championship game)

= 1/20 = 0.05

D) P(SEC or ACC having a team I championship game)

= (10+8-1)/20 = 0.85

E) P(championship game wont have any team from these two conferences) =1-0.85 = 0.15

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