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). What is the probability the ACC and SEC will both have teams in the championship game? Round your answer to 3 decimals.

Answer 1

Concepts and reason

The probability is the number that represents the chance or likelihood that a particular event will occur. The probabilities can be termed as proportions that range from 0 to 1 and also they can express as percentages from 0% to 100%.

Fundamentals

The formula for the mathematical probability is as follows:

$P\left( {{\rm{Event}}} \right) = \frac{{{\rm{Favourable number of cases}}}}{{{\rm{Total number of cases}}}}$

From the information, observe that the following events.

Consider A is the event that represents the Atlantic Coastal Conference.

Consider B is the event that represents the South Eastern Conference.

The number of times the Atlantic Coastal Conference will rank first is 10 times.

The number of times the South Eastern Conference will rank second is 8 times.

The number of times that both teams have had in the championship game is 1 time.

The total number of years is 20.

The calculation of the required probability is as follows:

$\begin{array}{c}\\P\left( {A \cap B} \right) = \frac{{{\rm{Favourable number of cases}}}}{{{\rm{Total number of cases}}}}\\\\ = \frac{1}{{20}}\\\\ = 0.05\\\end{array}$

Ans:

The required probability is 0.05