Statistics Problem

[EE2006]

I have a little statistics problem I want to figure out, and I was hoping some people here may be able to help. After seeing all the good responses to the Birthday Problem thread, I figure someone might be able to help me.


You have 5 teams, broken up as follows:

Team A - 3 males, 3 females
Team B - 3 males, 3 females
Team C - 3 males, 3 females
Team D - 3 males, 3 females
Team E - 1 male, 1 females


There will be 4 groups formed at random from these teams:

Group A - 6 males
Group B - 7 males
Group C - 6 females
Group D - 7 females


I have two questions based on this:

(1) What is the likelihood of all 3 males (or all 3 females) from one team all ending up in the same group?

ex. All 3 males from Team A end up in Group A

(2) What is the likelihood that all 3 males from one team will end up in one group AND all 3 females from one team will end up in one group, while no other team placing either 3 males or 3 females in one group?

ex. All 3 males from Team A end up in Group A
All 3 females from Team A end up in Group C
All other teams are split up


I hope I worded the second question well, if you need any clarification just let me know. Thanks in advance for any answer you can give.

 

[Joe4]

You wouldn't be asking us to do your homework for you now, would you?

 

[EE2006]

You wouldn't be asking us to do your homework for you now, would you?

Not unless they have started handing out homework to people who are no longer in school.

This question comes from a real-life observation. Scheduling for the tournament was done by Team A, and they were the only ones who were lucky enough not to be split up. I thought it was interesting, and just wanted to see the numbers on it.

 

[Joe4]

I was a Mathematics and Economics major in college, and I hated doing statistics then (I always preferred Calculus)!

I can't imagine doing it for fun when you don't have to, but I'm sure a few people will take up your challenge.

 

[EE2006]

Being an Engineer, I also have a natural leaning towards Calculus over Statistics. Having said that, as a huge sports fan and a born numbers guy, I do appreciate statistics.

My problem is that I usually don't know the correct approach. Once Eric got the ball rolling in the Birthday Problem thread, I could extend the idea in many different directions. It's getting that first idea going that usually stumps me.

 

[Andrew Fergus]

Hi

Here's my take on your question. What are the chances of 3 males from the same team ending up in the same group?

Once you have your first male from a team in a group (lets say of 6) it comes down to the probability of selecting the other two guys from that team in one of the remaining available slots in that group.

Assuming the groups are divided purely into males and females, the chances of selecting a 2nd male from the first team in the same group (of 6) is 1/12 + 1/11 + 1/10 + 1/9 + 1/8 which adds to about a 51% probability. The chances of selecting a 3rd male from the same team, after a 2nd person has been added to the same group, is 1/11 + 1/10 + 1/9 + 1/8 which is about a 43% probability. Multiplying the 2 together gives a probability of about 22% of all 3 guys from the same team ending up in the same group (of 6).

The probablity would be higher for 3 guys ending up in the same group of 7 - if you started with that one first. I suspect the probablities would also be different if each group selected a person in turn, instead of picking 6 guys for Group A and then the rest automatically go into Group B (this later method is the method I assumed in my calculation).

Hopefully I have my maths right - if not I'm happy to be guided as to where I went wrong.

Cheers, Andrew

 

[Joe4]

Being an Engineer, I also have a natural leaning towards Calculus over Statistics. Having said that, as a huge sports fan and a born numbers guy, I do appreciate statistics.

Well, sports stats, that's a whole different ball game than probability! I love sports stats too. I was calculating my batting average and ERA myself back in the third grade. I used to buy baseball, football, and hockey cards for the numbers on the back, not the pictures on the front... :wink:

 

[Greg Truby]

I used to buy baseball, football, and hockey cards for the numbers on the back, not the pictures on the front... :wink:
~jm14

Oh, you mean the side with the picture was the front?!

 

[Richard Schollar]

I used to buy baseball, football, and hockey cards for the numbers on the back, not the pictures on the front... :wink:
~jm14

Oh, you mean the side with the picture was the front?!

They had pictures on the Front?!?!??!

 

[Lewiy]

Probability of an event = (Number of ways the event can occur) / (Total number of possible combinations)

Now the question is: How many combinations of different males on different teams can there be? My brain stops working here.