There are 32 teams in the NFL. 16 of them are in the AFL. The other 16 are in the NFC. At the beginning of the season Julia tried to predict the teams that would be in each Conference championship by randomly drawing 4 teams (2 AFC teaams and 2 NFC teams) from 2 hats. What is the probability that the 4 teams she selected are the same 4 teams in each conference's championship?
I came up with 1/16,334
Would that be correct?
Thank you!
The number of final four team selections
= C(16,2)*C(16,2) , (choose 2 from AFL and 2 from NFC)
= 120*120 = 14400
one of these will be the correct one,
so prob = 1/14400
(how did you get 16334 ?)
To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Julia selects 4 teams from 32, and each selection reduces the number of available teams. Therefore, the total number of outcomes can be calculated as follows:
(32/1) * (31/1) * (16/1) * (15/1) = 14,880
Favorable outcomes:
To have the same 4 teams in each conference's championship, Julia must select 2 AFC teams and 2 NFC teams. We can calculate the number of favorable outcomes as follows:
(16/2) * (15/1) * (16/2) * (15/1) = 3600
Probability:
The probability is equal to the number of favorable outcomes divided by the total number of outcomes:
Probability = Favorable outcomes / Total outcomes = 3600 / 14,880 = 0.242
So, the correct probability of Julia selecting the same 4 teams in each conference's championship is approximately 0.242 or 24.2%.
Therefore, your initial calculation of 1/16,334 is not correct.