I wonder if the phrase they were playing around with was not "picked randomly" but rather the "uniformly distributed" phrase. I assume you are recalling the question from memory. Could they have said, "distributed uniformly" instead of "uniformly distributed"? Are you sure you remember the exact phrase they used? Could it have been "dispersed uniformly"?


Was this their words or your interpretation?
If they asked whether the cards would be distributed or dispersed uniformly in the new deck they might mean it to be interpreted as a question about a quality of the deck that results as the specific outcome of the "shuffle". For example, suppose the shuffled deck happens to turn out AAAA,2222,3333,...,KKKK. Is that specific deck one whose cards you would describe as being distributed uniformly? I don't think so. Yet it's a perfectly possible outcome of the random shuffle.

This seems to me the most reasonable view that would allow for a "No" answer. Recognizing that clumps of cards often occur in randomly shuffled decks is the kind of thing I'd think a hedge fund person ought to be aware of. Randomly shuffled decks can produce bad runs of cards and black swans can sink hedge funds.


If they are just playing on the ambiguity of the phrase, "picked randomly" because the phrase ought to be followed by a specified probability distribution to be well defined, then "No" is not really a correct answer to the question. The correct response would be to point out that the phrase "picked randomly" and therefore the question as a whole is not well defined.

PairTheBoard

I agree. It's very likely that something has been lost in the OP's recounting of the question.

The interviewee was actually a friend of mine so it's possible that he might've missed something. I myself can't find any reason for why the new deck isnt uniformly distributed.

Thanks for the replies anyway.

this question is pretty ******ed. Technically, since the deck is new, the "shuffled" deck you make will not be uniform because you will know certain things about the distribution. Because the new deck is arranged hearts, spades, diamonds, clubs, if you take the first card out of the bottom of the new deck, then obviously the bottom card of your shuffled deck cannot be the ace of hearts since its still at the top of the new deck. goldman sachs math questions are usually pretty straightforward, so i really don't understand wtf is up with this one.

This is pretty good.

Obviously the best answer will then be: 'Not if you pay attention.'

[IMG]http://img2.*********************/uploads/5aa721b6df.jpg[/IMG]

which one is it under?

TProbability puzzle

This puzzle can be adequately solved by writing a MC(Monte Carlo analysis) computer program using a pseudo random number generator in conjunction in the program to simulate the cards. Then a sufficient number of iterations (trials) should be run to average out short term effects (perhaps a million iterations or more – no big deal on today’s high speed PCs). Assuming the legitimate deck contains 52 cards; create an array with 52 cells in it; i.e. CARD(j), j = 1 to 52; and initialize each CARD(J) to zero . At the end of each iteration, do a top down count until the King of Hearts is found; for example, if during the count down the 29th card happened to be the King of Hearts; then increment the array cell CARD(29) to CARD(29) + 1. After sufficient trials (iterations); examine the numerical value of each CARD cell. If the process in question is truly random; then each CARD (J) cell should have almost the same numerical value in it (within a statistical calculated range). That is with the law of Large Numbers, Standard Deviation, or whatever. I’m sure that if this is if done properly it is a random process operation.


I have to go to my PC trouble shooting class -- so I'm posting a quick reply -- excuse me -- I'm already late Carl_WILLIAM