My Math Forum mathematical expectation of how many times to get all cards

 January 12th, 2012, 02:52 AM #11 Newbie   Joined: Jan 2012 Posts: 8 Thanks: 0 Re: mathematical expectation of how many times to get all ca it takes at least 6 times to get all cards i think the expected values is 6*K6 + 7*K7 + ... + n*Kn Kn is possibility you get all cards at nth time. n->infinite
 January 12th, 2012, 04:20 PM #12 Global Moderator   Joined: May 2007 Posts: 6,684 Thanks: 658 Re: mathematical expectation of how many times to get all ca The problem statement is unclear. There are six cards. A card is picked at random. IS THE CARD PUT BACK??????????? If not, then the solution is the trivial one that I suggested. If it is put back, then it is an interesting problem.
January 12th, 2012, 05:38 PM   #13
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Re: mathematical expectation of how many times to get all ca

Quote:
 Originally Posted by mathman The problem statement is unclear. There are six cards. A card is picked at random. IS THE CARD PUT BACK??????????? If not, then the solution is the trivial one that I suggested. If it is put back, then it is an interesting problem.
there are 6 kinds of cards, and number of each kind of card is unlimited

January 13th, 2012, 12:44 AM   #14
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Re: mathematical expectation of how many times to get all ca

Quote:
Originally Posted by newme
Quote:
 Originally Posted by mathman The problem statement is unclear. There are six cards. A card is picked at random. IS THE CARD PUT BACK??????????? If not, then the solution is the trivial one that I suggested. If it is put back, then it is an interesting problem.
there are 6 kinds of cards, and number of each kind of card is unlimited
Say, what?

So...is each card is marked uniquely and chosen with replacement? (i.e, when a card is chosen, is it put back in the group, possibly chosen again?) These are the kinds of things we need to know to solve the problem.

A well-formed question gets a well-formed response...not being harsh, that's just the way it is...[color=#00BF00]mathman[/color] raises valid concerns that must be addressed before the question makes sense...otherwise people are really just guessing at what you mean. Help us to help you.

January 13th, 2012, 08:50 AM   #15
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Re: mathematical expectation of how many times to get all ca

Quote:
 Originally Posted by MarkFL So...is each card is marked uniquely and chosen with replacement? (i.e, when a card is chosen, is it put back in the group, possibly chosen again?) These are the kinds of things we need to know to solve the problem.
I'll answer on his behalf: yes, oui, si, ...

1- take 6 cards at radom from a regular 52-card deck
2- throw the other 46 in the garbage
3- pick a card (from the li'l pack of 6, of course; anyway the others are in the garbage...)
4- LOOK at the card, write down what it is
5- put it back in the li'l pack of 5 (so you now have 6), and shuffle 'em well
6- repeat steps 3 to 5 five more times (note that 5th step need not be done at end!)

What is the probability that you wrote down 6 different cards?

January 16th, 2012, 06:23 PM   #16
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Re: mathematical expectation of how many times to get all ca

Quote:
 Originally Posted by Denis I'll answer on his behalf: yes, oui, si, ... 1- take 6 cards at radom from a regular 52-card deck 2- throw the other 46 in the garbage 3- pick a card (from the li'l pack of 6, of course; anyway the others are in the garbage...) 4- LOOK at the card, write down what it is 5- put it back in the li'l pack of 5 (so you now have 6), and shuffle 'em well 6- repeat steps 3 to 5 five more times (note that 5th step need not be done at end!) What is the probability that you wrote down 6 different cards?
sorry for my poor english.
i think this is what i mean.

 January 16th, 2012, 06:45 PM #17 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 Re: mathematical expectation of how many times to get all ca Well then, probability is: 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 5 / 324
 January 17th, 2012, 02:27 PM #18 Global Moderator   Joined: May 2007 Posts: 6,684 Thanks: 658 Re: mathematical expectation of how many times to get all ca The problem statement originally was unclear. There are two different problems. 1) (Which has been answered) what is the probability that you will get six different cards when selecting six cards at random? 2) (Difficult) What is the average number of selections required to get six different cards?
January 17th, 2012, 11:56 PM   #19
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Re: mathematical expectation of how many times to get all ca

Quote:
 Originally Posted by Denis I'll answer on his behalf: yes, oui, si, ... 1- take 6 cards at radom from a regular 52-card deck 2- throw the other 46 in the garbage 3- pick a card (from the li'l pack of 6, of course; anyway the others are in the garbage...) 4- LOOK at the card, write down what it is 5- put it back in the li'l pack of 5 (so you now have 6), and shuffle 'em well 6- repeat steps 3 to 5 five more times (note that 5th step need not be done at end!) What is the probability that you wrote down 6 different cards?

sorry for my poor english.
i think this is what i mean.

January 18th, 2012, 01:40 AM   #20
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Re: mathematical expectation of how many times to get all ca

Quote:
 Originally Posted by mathman The problem statement originally was unclear. There are two different problems. 1) (Which has been answered) what is the probability that you will get six different cards when selecting six cards at random? 2) (Difficult) What is the average number of selections required to get six different cards?
second one.

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