Word probability problem

Question

I am trying to solve this probability problem:

Suppose there are 100 students total in your year at UCLA. Each tutorial group consists of 10 students. What is the probability that for the next course you are in a tutorial group with none of the students that were in your tutorial group for Basic Statistics (assuming, of course, that students are assigned to groups in a random manner)?

Now when I read it I think that it could be solved by just calculating the probability complement of odds of meeting 10 people out of 100 which would be:

1 -10/100 = 0.9

However, this question is from a material which discusses binomial distribution, and combinations and permutations, so I feel like I miss something. Any ideas?

Answer 1

There are ${99\choose 9}$ ways to assign studuents (other than your self) to join you in any study session.

And ${90\choose 9}$ that include none who are in your stats study session.

$\frac {{90\choose 9}}{{99\choose 9}}$

Answer 2

Hint:

• there are $9$ other people in your basic statistics class and $90$ students who are not

• What is the probability the first student you meet in your new class was not in your basic statistics class?

• If the first student you meet in your new class was not in your basic statistics class, what is the conditional probability that the second student you meet in your new class was not in your basic statistics class?

• If the first two students you meet in your new class were not in your basic statistics class, what is the conditional probability that the third student you meet in your new class was not in your basic statistics class?

• $\cdots$

• What is the conditional probability that all nine students you meet in your new class were not in your basic statistics class?