Problem Solving

tnaim wrote:the answer to this question is B. B is sufficient on the ground that you can have RW or WR (red, white) or (white, red).
I could not understand why order would matter here. We don't necessarily have the following two conditions:
1) no replacement: the question does not mention that the balls are returned back
2) I can take out two marbles at the same time -- grab two at a time and not one after another. in that case, why would order matter? as long as I have two balls, each of which is of a different color, then that's all that matters.

i may not have made myself clear enough here.

the issue isn't about the inherent restrictions of the problem; the issue is about the approach that you take to solving the problem.
what i mean here is that, in a lot of cases, there are many ways to approach the same problem -- in fact, just about any problem that can be phrased as a "order doesn't matter" problem can also be rephrased in terms such that order does matter (although the reverse is normally not true). for instance, if you are picking a group of three people from A, B, C, D, E, F, G, and you are interested in the probability of picking the group A, B, C, then there are (at least) two ways that you can calculate the probability:
(1) using an "order doesn't matter" approach, you can calculate a probability of 1 / (7c3).
(2) using an "order does matter" approach, you can calculate that the probability of picking A then B then C is (1/7)(1/6)(1/5). since this is only one possible order, though, you must repeat the process for the other five orders (ACB BAC BCA CAB CBA), so the total probability is six times this product.
each one of these calculations will yield the same probability.

in any other problem that can be phrased as "order doesn't matter", you are going to have the same two options.

so, here's the point: in order to use consecutive probability multiplication, you MUST INTERPRET THE PROBLEM in such a way that order matters.
you'll notice that, in the derivations above, the first does not use consecutive multiplication (because it can't -- that interpretation uses order-doesn't-matter), but the second does.

aditya_velma wrote: Ron,
I have a question here. I understood when u said that certain problems may require order etc.
In the problem https://www.beatthegmat.com/combinatorics-t71136.html

when I say (90/800)*(1/600), why shouldn't I add (90/600)*(1/800) to this? Is it because we are selecting 1 piece each from 800 and 600 respectively, instead of 2 pieces from (800+600) for the total number of conditions?

please post this question on that thread (not this one) and send me a private message to the new post; then i'll answer it in detail. thanks.

the short answer is that, when you consider "order matters", you settle on one order in which you are going to pick the components of the problem, and then calculate all of the probabilities according to that order.

Hi MrGaga,

Answering these types of questions depends on what the question ASKS FOR.

We'll work with the example that you're going to throw 2 dice.

Since each of the two dice is its own outcome, the total possible number of outcomes = (6)(6) = 36, since the ORDER of the dice MATTERS. The probability of rolling two 1s = (1/6)(1/6) = 1/36.

How exactly did you calculate 1/21?

GMAT assassins aren't born, they're made,
Rich