There are 32 teams in the NFL. Sixteen of the teams are in the American Football Conference (AFL) and the other 16 teams are in the National Football Conference (NFC). At the beginning of the season, Julia tried to predict the teams that would be in each conference's championship by randomly drawing 4 teams (2 AFC teams and 2 NFC teams) from a hat. What is the probabliliy that the 4 teams she selected are the same 4 teams that will be in the conferences' championships? Express your answer as a common fraction.
This doesn't make any sense! Please explain!
can somebody please help me!?! this is urgent!
2/4 as a fraction
how can i do a long mathemathic that deal with probability and equal 13?
1/4 is the answer
Sure, let me explain.
In the NFL, there are a total of 32 teams, divided into two conferences: the AFC (American Football Conference) and the NFC (National Football Conference). Each conference consists of 16 teams.
At the beginning of the season, Julia randomly draws 4 teams from a hat - 2 teams from the AFC and 2 teams from the NFC. She wants to know the probability that the 4 teams she selected are the same 4 teams that will be in the conferences' championships.
To understand the probability, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
The total number of possible outcomes can be determined by considering the number of ways Julia can choose 2 teams from each conference. For the AFC, she can choose 2 teams out of 16, which can be calculated using the combination formula, represented as C(16, 2). Similarly, for the NFC, she can choose 2 teams out of 16, again using the combination formula, represented as C(16, 2).
Therefore, the total number of possible outcomes is C(16, 2) * C(16, 2).
Now, we need to calculate the number of favorable outcomes, which is the number of ways Julia can select the same 4 teams that will be in the conferences' championships. Since we already know that there are 16 teams in each conference, she has to choose 2 teams from each conference in a specific order. Therefore, the number of favorable outcomes is 1.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 1 / (C(16, 2) * C(16, 2))
Hence, the probability that the 4 teams Julia selected are the same 4 teams that will be in the conferences' championships is 1 / (C(16, 2) * C(16, 2)), where C(n, r) represents the combination formula to choose r items from a set of n items.