Question

4. Suppose 8 teams qualify for the ADA football tournament quarterfinals. The quarterfinal pairings will be determined by a random draw in which any team can be paired with any other. The teams are Evils, Back Line, Lyceum United, Undefeated Armada, MBA Eagles, Front Line, Defeated Armada, Angels. What is the probability that Evils will play Back Line? What is the probability that Back Line will be paired with Undefeated Armada and MBA Eagles will be paired with Lyceum United?

Answer 1

No. of ways that any one of the 8 teams will be paired with another team = = 28 ways = n(S).

Let A be the event that Evils plays Back Line.
A can happen in 1 way = n(A).
Therefore, Prob.(A) = n(A)/n(S) = 1/28 = 0.0357

Let B be the event that Back Line plays with Undefeated Armada and C be the event that MBA Eagles plays Lyceum United.
Both B and C can happen in 1 way.
Hence, Prob.(B) = 1/28 and Prob.(C/B) = 1/27
Therefore, Prob.(B intersection C) = Prob.(B) x Prob.(C/B) = (1/28).(1/27) = 0.0013