Strange Conceptual Anomaly in Probability

Imagine a bag containing 4 Red and 4 Blue balls. The experiment is to take out 2 balls at a time, without replacement.

The sample spaced would be C(8,2) as we need to select 2 balls out of the 8 that are there.

The equally likely outcomes are RR, BB, RB and BR. Each of these outcomes is equally likely because each has a probability of occurring as 1/4.

Here are 2 things I am unable to understand here:

1) If the questions asks, what is the probability of getting both the balls of different colours in a single draw of 2 balls, then shouldn't the answer be =1/4??

2) If my approach is wrong, then please explain why?

3) If my approach is right, then where have we made use of the sample space? I mean then, in that case, even if we have a 1000 Red and 1000 balls, the equally likely outcomes of the experiment defined as selecting 2 balls at once will be RR, BB, RB and BR.


Please help someone!!!

varun.v4 said:

Imagine a bag containing 4 Red and 4 Blue balls. The experiment is to take out 2 balls at a time, without replacement. The sample spaced would be C(8,2) as we need to select 2 balls out of the 8 that are there.
The equally likely outcomes are RR, BB, RB and BR. YES! Each of these outcomes is equally likely NO!

Click to expand...

This is without replacement. So the elementary events cannot be equal.
\(\displaystyle \begin{align*} \mathcal(P)[RR]&=\dfrac{4\cdot 3}{56}\\ \mathcal(P)[RB]&=\dfrac{4\cdot 4}{56}\\ \mathcal(P)[BR]&=\dfrac{4\cdot 4}{56}\\\mathcal(P)[BB]&=\dfrac{4\cdot 3}{56}\end{align*}\)