SOLUTION: if you have 8 teams, what are the odds of two people joining a league being drafted on the same team

Question 894137: if you have 8 teams, what are the odds of two people joining a league being drafted on the same team

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the probability is going to be 1/8.
here's why.
assume only 3 teams.
assume the teams are ABC
you have 2 people, each of which can land on any of the teams.
the possible pairings you can get will be 3*3 = 9
person 1 gets the first letter
person 2 gets the second letter.
the letter designates the team.
the possible pairings are:
AA *****
AB
AC
BA
BB *****
BC
CA
CB
CC *****
out of the 9 possible pairings there are 3 pairings where person 1 and person 2 are on the same team.

remember.
the first column represents the team that person 1 gets.
the second column represents the team that person 2 gets.

3 out of 9 is the same as 1 out of 3.

use that logic with the 8 teams and you get the probability that they will be on the same team is 8/64 which is equal to 1/8.

a sample of a subset of what that will look like is shown below:
the teams are ABCDEFGH
the possible pairings are:
AA *****
AB
AC
AD
AE
AF
AG
AH
BA
BB *****
BC
BD
BE
BF
BG
BH
etc 8 times in all.

in the first set of 8, 1 pairing had both persons on the same team (team A).
in the second set of 8, 1 pairing had both persons on the same team (team B).

this will occur 8 times out of 64 which results in 1 out of 8 which give you a probability of 1/8.

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