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!

To find the probability that Julia's randomly drawn 4 teams are the same 4 teams that will be in the conferences' championships, we need to consider the total number of possible outcomes and the number of favorable outcomes.

To start, we know that there are 16 teams in each conference, AFC and NFC.

When Julia draws the first team from the hat, there is a 1 out of 16 chance (1/16) for her to choose a team from the AFC conference that will be in the championship.

After her first draw, she has chosen a team from the AFC conference, leaving 15 teams remaining in that conference. Now, there is a 1 out of 15 chance (1/15) for her to choose another team from the AFC conference that will be in the championship.

To find the probability of both events happening (choosing an AFC team in the first draw and another AFC team in the second draw), we multiply the individual probabilities:

(1/16) * (1/15) = 1/240

The same logic applies to selecting teams from the NFC conference. There is a 1 out of 16 chance (1/16) for her to choose a team from the NFC conference in the first draw and a 1 out of 15 chance (1/15) for her to choose another NFC team in the second draw.

Again, multiplying these probabilities gives:

(1/16) * (1/15) = 1/240

Now, to find the probability of both events happening (choosing an AFC team in the first draw and another AFC team in the second draw, as well as choosing an NFC team in the first draw and another NFC team in the second draw), we multiply these probabilities once more:

(1/240) * (1/240) = 1/57,600

Therefore, the probability that the 4 teams Julia selected are the same 4 teams that will be in the conferences' championships is 1/57,600.

Sure, I can explain the problem to you.

The problem asks for the probability that Julia randomly selects the exact same four teams that will end up in the championships for both the American Football Conference (AFC) and the National Football Conference (NFC).

To find the probability, we need to consider the total number of possible outcomes and the number of successful outcomes.

There are 32 teams in the NFL, so the total number of possible outcomes is the number of ways to choose 4 teams out of 32, which can be calculated using the combination formula:

C(32,4) = 32! / (4!*(32-4)!) = 32! / (4!*28!) = (32*31*30*29) / (4*3*2*1) = 27,040

Now, we need to determine the number of successful outcomes, which is the number of ways to choose 2 teams out of 16 for each conference.

For the AFC, there are C(16,2) ways to choose 2 teams out of 16, which is given by:

C(16,2) = 16! / (2!*(16-2)!) = 16! / (2!*14!) = (16*15) / (2*1) = 120

Similarly, for the NFC, there are also C(16,2) = 120 ways to choose 2 teams out of 16.

Since Julia needs to select 2 teams from both the AFC and the NFC, to find the number of successful outcomes for the entire scenario, we multiply the number of successful outcomes for each conference together:

Successful outcomes = number of successful outcomes for AFC * number of successful outcomes for NFC = 120 * 120 = 14,400

Finally, we can calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes:

Probability = Successful outcomes / Total outcomes = 14,400 / 27,040 = 9/17

So, the probability that Julia randomly selects the exact same four teams that will be in the conferences' championships is 9/17, which is approximately 0.529.