On page 90 of the Word Translations 4th Ed. I learned about a strategy to compute probability with a domino effect.

The Domino Effect
--
Sometimes, the outcome of the first event will affect the probability of the subsequent event.


It shows that the CORRECT way to compute probability for picking a RED ball out of a set of 3RED+7OTHERS on each of the first 2 tries. The probably given in the answer is 1/15 for this problem.

However, when I apply a probability tree method to this problem, the result comes up with 8/15:

The tree is built similarly as the example with the values used in the red ball problem:

(Red first:3/10 x Red Second:2/9) + (Red first: 3/10 x Non-Red second:7/9) + (Non-Red first:7/10 x Red second: 3/9) = 8/15

When I use the "1-x trick", I get: (Non-Red First: 7/10 + Non-Red Second: 6/9) still out of the probability tree which gives the same result: 1 - 7/15 = 8/15

So the result comes out with 8/15 in both case while the book reports that it should be 1/15.

While reviewing the domino solution given, it is still unclear to me why the method skips the case where a non-Red ball can be picked up the first time.

Can you please point me to the error I am making or if there is something I didn't apply correctly? Thank you in advance.

Hi ldesegur,

Your problem isn't the computations, it is the interpretation of the problem. The problem says "on each of the first 2 tries" and what you have computed is for "on either of the first 2 tries".

Thus, for example, you should stop at
(Red first:3/10 x Red Second:2/9) = 1/15

Thanks and shame on me. I need to be more careful about reading the questions.

Good lesson to learn. Thanks John..

_________________
Tim Sanders
Manhattan GMAT Instructor