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Probability Help

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by GMATinsight » Thu Jan 21, 2016 10:44 am
g3lo wrote:Hi all,

Was hoping one of you could help me wrap my mind around the below;

presuming B occurs, the probability that A occurs is AnB/B

Thank you,
g3lo
Yes you are right... It's conditional probability. You can read in detail as Baye's theorem/Conditional probability.
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by g3lo » Thu Jan 21, 2016 10:57 am
I guess my question was, how do they set-up the equation using the wording. For some reason, it does not sink in. I do not want to resort to memorizing if I can break it down and understand it.
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by [email protected] » Thu Jan 21, 2016 3:00 pm
Hi g3lo,

Conditional probability is exceptionally rare on the GMAT (I'll bet that you don't see it at all on the Official GMAT). In the event that you see a Quant question that 'hints' at conditional probability, you will almost certainly be able to answer the question using simpler probability concepts and/or permutations or combinations.

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by DavidG@VeritasPrep » Fri Jan 22, 2016 9:08 am
g3lo wrote:Hi all,

Was hoping one of you could help me wrap my mind around the below;

presuming B occurs, the probability that A occurs is AnB/B

Thank you,
g3lo
The concept is more important than the derivation of the notation. (And, thankfully, the concept really isn't complicated, at least for what we'll need on the GMAT.)

Imagine you have a bag of marbles. There are 3 red and 5 blue marbles and no other kinds of marbles. Say we select two marbles at random and we want to know the probability that we select two red marbles.

The scenario when we select a red marble on the first pick, we'll call: Event A
The scenario when we select a red marble on the second pick, we'll call: Event B

First, find P(A): There are 3 red marbles and 8 total marbles, so P(A) = 3/8

Next find P(B|A): The notation here simply means the probability that B will occur, given that A has occurred. So if A occurred, then we selected a red marble with the first pick. In this case, there will be 2 red marbles remaining and 7 total marbles remaining, meaning that P(B|A) = 2/7.

And the probability that we select a red on both picks is P(A) * P(B|A) = (3/8) * (2/7)

The most important thing is to make sure you note that the composition of the bag's marbles changes with each selection. (When you're solving this on your own, you don't need to use the notation.)
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by g3lo » Fri Jan 22, 2016 4:47 pm
Thank you both for the answers!

Rich, I sent you a PM, could you kindly reply when you get the chance?

Best,
g3lo
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by [email protected] » Fri Jan 22, 2016 7:12 pm
Hi g3lo,

I've responded to your PM; if you have any additional questions, then you can feel free to contact me directly (by email or by PM).

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