Probability

[Jefferson]

HI all,
What are some formal ways (using perms/combs, or multiplying fractions like normal probability questions, etc) to solve the following problem.


A set of 4 marbles containing:
2 Red
1 Blue
1 Green
- is placed in a bag. Michelle selects one marble, and then another without replacing it.
Given that one of her marbles is Red, find the probability that the other one is also red (Answer: 1/5).


I listed all the possibilities, then crossed off the ones which doesn't contain Red marble (since we know that at least 1 marble is red).

R₁ R₂
R₁ B
R₁ G

R₂ R₁
R₂ B
R₂ G

B R₁
B R₂
B G

G R₁
G R₂
G B

This leaves 10 cases, 2 of which has 2 red marbles.
Hence 2/10 = 1/5.

Wasn't very happy with the way I did it (hopefully it's not just a coincidence), but also it'll be difficult to pull off if there were 3 selected items or perhaps more marbles to increase the sample space.

Any suggestions? Thanks!

[RuiAce]

Not really.

The question is actually conditional probability, which isn't even in the current HSC syllabus (although it is in the new one). Tree diagrams can be used to help address this conditional probability. (Note that tree diagrams virtually mean the same thing as your "multiplying fractions" approach.)

But for the current syllabus, I would probably have gone with listing as well.

No combinatorial approach stands out to me at first glance, but I can't say for sure because I didn't give it much thought, since this is the 2U thread after all.