Question

Teresa and Julia are among 10 students who have applied for a trip to Washington, D.C. Two students from the group will be selected at random for the trip. What is the probability that Teresa and Julia will be the 2 students selected?

Answer 1

This is a combination problem.

nCr is the general formula
n! / ( (n - r)!r!)

n = 10
r = 2
10! / [8! 2! ]

10*9/2 = 45

So the probability they will be the students picked is 1/45.

Answer 2

I get how you got 45, but where did the 1 come from?

Answer 3

1 just indicates that for every 45 possibilities of student combinations, the combination of those two girls will only occur (in theory) once.

Answer 4

It's just the reduced version of 2/90.

2/90=1/45

Answer 5

Why is it 2/90

Answer 6

This problem is sampling without replacement. The hypergeometric distribution applies.

Answer 7

There are 10 students to pick from the first time. To determine the second student, there will be 9 left to choose from. So 10*9 = 90.

Since there are two girls in the problem, it is 2/90.

Answer 8

oh i see. Thanks a Bunch :D (Im reviewing for state testing tomorrow)

Answer 9

Sure, no problem. Best of luck!

Answer 10

Not quite sure where you got 2*10*9 from. Even using the hg calculation, it would be (2 choose 2) * (8 choose 0) / (10 choose 2) .... which results in 1/45

Answer 11

The hypergeometric calculation gives a probability of choosing Teresa and Julia as follows:\[P(T+J)=\frac{\left(\begin{matrix}2 \\ 2\end{matrix}\right)\left(\begin{matrix}8 \\ 0\end{matrix}\right)}{\left(\begin{matrix}10 \\ 2\end{matrix}\right)}=\frac{2}{10\times 9}=\frac{1}{45}\]
Sorry for mistake in previous posting (now deleted).