basic conceptual error in Schweser? conceptual, different, shuffle

dontknow1987

I was looking at the paragraph at the top of page 143 in the Schweser Level III Book 1, and my basic sense of probability was offended. I know there are lots of errata in these things, but this is different because it can’t be a typo– it’s too specifically and adamantly wrong.
Basically, it states that if you draw a card from a normal 52 card deck of cards, you can know that the chance of it being a diamond is 1/4 (true). Then they state that if you take several decks of cards and shuffle them all together, then draw 52 cards at random, then draw a random card from those 52 cards, “we don’t know the odds of selecting a card from one of the four suits, because we don’t know the number of each suit in the sample.” FALSE FALSE FALSE! If you know the makeup of the decks of cards, then any random draw, whether just drawing one card or drawing 52 and then picking one of those at random will be a random sample of the original population, so it should still have a 1/4 chance of being a diamond.
I know it’s not very relevant from a test taking perspective (it’s not a math question but an explanation of a behavioral finance point) but I find it highly repugnant that such a basic mistruth could be penned by a schweser writer. Makes me doubt the quality of the writers/editors and makes me worry that I am reading bad info that I am not detecting.
Am I missing something here?

skycfa

I think what they are trying to say is that if you draw 52 cards randomly out of the set, you are creating an entirely new population. Of this new population, you have no idea what the probability of drawing a particular suite is. It seems like you may be looking to much into this. Schweser is not perfect but they wouldn’t make a mistake on something that simple,

RobertA

But you do! If you do this a million times (draw 52 then draw 1 of the 52) your results will converge on 25% diamonds no matter what.
That’s like saying you don’t know the probability of drawing a diamond from a single deck of randomly shuffled cards because the diamonds might be all bunched up at the end and you don’t know the makeup of the top few cards in the deck??

needhelp1700

I can’t agree with THA, though I agree with maratikus that I’m talking about unconditional probability. The thing is, this problem never gets into the realm of conditional probability, because you never gain any information. You can’t “go Bayesian” without some additional piece of information, and taking a random sample of a random sample of a population is not grounds for using conditional probability (or to be more correct, it is not grounds to abandon the ramifications of unconditional probability).
Here’s another way to state my point. Lets say there is a bag with 50 red marbles and 50 blue marbles in it. If you draw one, there is a 50% chance of it being red, of course. What Schweser and THA are saying is that if you reach two hands into the bag and grab a handful of marbles with one hand, then, without peeking, you use your other hand to pluck a single marble from the handful, you cannot know the probability of it being red or blue, because you don’t know how many red/blue marbles you picked up before selecting one. Of course in reality, any manipulation of the marbles is irrelevant; when you draw that first marble out and look at it, it has exactly a 50% chance of being red.
The Reductio ad absurdum of the spurious leap to conditional probability is this. Using THA and Schweser’s argument, if you take a 52 card deck and draw a single random card from it, the probability is not 25% that it’s a diamond, it would be 0% if it is not a diamond and 100% if it is a diamond. That is true in reality, but that misses the whole point of probability and random processes.
This reminds me of the Monty Hall problem, where people just don’t seem to come to consensus. Am I vox clamantis in deserto here, or does anyone agree with me? I just can’t believe anyone could read the Schweser paragraph in full and agree with it. I am still 100% convinced it is patently wrong as written.

whew1110

do not go by schweser. read what the book says. If that is exactly what the CFAI book says, even if you think it is wrong, for the 6 hours of the exam it is god’s truth. Keep it that way and do your research later.

Londonrocks

Yeah, I totally agree, cpk. Unfortunately, this isn’t a case of schweser misinterpreting CFA curricula, it’s just a case of them selecting an example out of thin air and being totally wrong about it IMO.
I’m just saying it makes me think the schweser writers/editors incapable of basic probability are probably not capable of adequately summarizing LIII curricula for me, so I guess I will stick with CFAI readings from here on out.

Penny-wenny

wonder what Schweser would say about the Monty Hall problem?

pacmandefense

Yeah, I guess I will just let this go.
Notenought, I think you’re right, but if that’s what they meant, they should have said “someone hands you a stack of 112 playing cards – you don’t know the mix of diamonds” not “you randomly sample playing cards where each suit represents 25% of the population – suddenly each suit does not have a 25% chance of appearing when a card is drawn from the random sample because you don’t know what specific cards are in the random sample.”
I guess it’s the gambler in me, but I always think in terms of betting. If you did the “Schweser sample” as discussed above, and you would give me =75 cents each time a non diamond was drawn and I would give you
I guess I can see what they mean, if that’s what they mean… it’s just not what they said.