Team game - pairing probability issue (non-academic problem)

So I'm playing a two team game.There are 20 players initially and we know that the makeup of team A is 16 players and team B is 4 players.

Assuming random selection), given each player is 'attached' to another player into pairs, in a way not related to the teams A or B, what is the probability of an A-A pair, a A-B pair and a B-B pair please?

Reply 1

BizzStrut

P(A) = 4/5
P(B) = 1/5
N = 20

P(A-A) = 4/5 * 4/5 = 1/5
P(A-B) = 4/5 * 1/5 = 4/25
P(B-B) = 1/5 * 1/5 = 1/25

So that's the probability for the first draws, I think. Where do I go from here?

edit: or is it different because there is now 1 less element in the set and so it's not the same probability multiplied by itself?

edit 2: yeah, this looks wrong. Please help! xD

(edited 7 years ago)

Reply 2

BizzStrut

I'd very much appreciate even a methodology here if an answer is too tedious :biggrin:

Reply 3

Cryptokyo

Original post by BizzStrut

I'd very much appreciate even a methodology here if an answer is too tedious :biggrin:

This is how I would approach the problem. After being selected a person is removed from the list of people that can be selected.
Therefore the following probabilities occur for the first draw:

P(AA)=\frac{16}{20}\times\frac{15}{19}=\frac{60}{95}

P(AB)=2\times\frac{16}{20}\times\frac{4}{19}=\frac{32}{95}

P(BB)=\frac{4}{20}\times\frac{3}{19}=\frac{3}{95}

Note that there are two permuations for the AB pairing as it can be paired AB or as BA.
Use this principle to now look at the question from a combination standpoint. Any further help needed just ask.

Cryptokyo

Quick Reply

Latest

Articles for you

How our community record system works

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

Team game - pairing probability issue (non-academic problem)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you