What is the Probability That Two Specific People Will Be on the Same Team?

[mamma_mia66]

Homework Statement

suppose that 35 people are divided in a random manner into two teams in such a way that one team contains 10 people and the other team contains 25 people. What is the probability that two particular people A and B will be on the same team.

Homework Equations

I don't have the answer on this problem , I am confused. Please help.

The Attempt at a Solution

35 people team C contains 10 people, so the chance to be in this team is 2/7
team D contains 25 people, so the chance is 5/7
when person A is divided in team C , then there is a chance for person B, to be also in this team, namely 9/34(1 person is already divided)
when person B is divided in team D, then there is a chance for person B, to be also in this team, namely 24/34
so there are 2 cases
case 1 has a chance of 2/7*9/34=18/238
case 2 has a chance of 5/7*24/34=120/238
together this is 138/238=69/119 (=0.58) that they are in the same team (the chance is always bigger than 50%)

 

[kasse]

I get the same answer.

 

[mamma_mia66]

Then it is okay. Thanks.