probabiliy of equal cards

Printable View

June 3rd 2012, 01:12 PM
billobillo

probabiliy of equal cards

If we have two decks of 52 cards each that are shuffled randomly.And if the positions of cards for each deck are numbered from 1 to 52.
What is the probability that these two decks contain the same card at the same position.
June 3rd 2012, 01:55 PM
Plato

Re: probabiliy of equal cards

Quote:

Originally Posted by billobillo

If we have two decks of 52 cards each that are shuffled randomly.And if the positions of cards for each deck are numbered from 1 to 52. What is the probability that these two decks contain the same card at the same position.

If a standard decks is well shuffled what is the probability that no card is in its original position?
June 3rd 2012, 02:50 PM
billobillo

Re: probabiliy of equal cards

Quote:

Originally Posted by Plato

If a standard decks is well shuffled what is the probability that no card is in its original position?

Well I guess your question is the same of mine, because having a non shuffled and a shuffled deck is like having two different decks.
June 3rd 2012, 03:00 PM
Plato

Re: probabiliy of equal cards

Quote:

Originally Posted by billobillo

Well I guess your question is the same of mine, because having a non shuffled and a shuffled deck is like having two different decks.

That is correct. So if $p$ is the probability of not having any card in its correct place then $1-p$ is the probability of at least one card in its correct place.

Do you know about derangements ?
June 3rd 2012, 03:32 PM
billobillo

Re: probabiliy of equal cards

Quote:

Originally Posted by Plato

That is correct. So if $p$ is the probability of not having any card in its correct place then $1-p$ is the probability of at least one card in its correct place.

Do you know about derangements ?

Actually I'm not a math specialist, I tried to solve it in a easy way and I got p=1.
A card in position 1 in deck 1 has probability 1/52 to be equal to a card in position 1 in deck 2.
And since we have 52 cards, then the probability to get two equal cards at same position is 52 * 1/52 = 1
Could it be p=1?
June 3rd 2012, 03:41 PM
Plato

Re: probabiliy of equal cards

Quote:

Originally Posted by billobillo

Actually I'm not a math specialist, I tried to solve it in a easy way and I got p=1.
A card in position 1 in deck 1 has probability 1/52 to be equal to a card in position 1 in deck 2.
And since we have 52 cards, then the probability to get two equal cards at same position is 52 * 1/52 = 1
Could it be p=1?

You cannot work this question with out derangements. As far as I know there is no other way.
Did you read the link I gave you?
Why were you given this problem to do?
June 3rd 2012, 04:11 PM
bjhopper

Re: probabiliy of equal cards

Two decks are shuffled. The first is the reference deck and I interpret that the question is what is the P that the second deck will have the exact same order as the first. I would answer 52 factorial is the number of possible events.P= 1/8*10^67
June 3rd 2012, 05:20 PM
Plato

Re: probabiliy of equal cards

Quote:

Originally Posted by bjhopper

Two decks are shuffled. The first is the reference deck and I interpret that the question is what is the P that the second deck will have the exact same order as the first. I would answer 52 factorial is the number of possible events.P= 1/8*10^67

You have got to be kidding!
June 3rd 2012, 11:13 PM
billobillo

Re: probabiliy of equal cards

Quote:

Originally Posted by Plato

You cannot work this question with out derangements. As far as I know there is no other way.
Did you read the link I gave you?
Why were you given this problem to do?

Yes I read the link, it contains a similar question about persons and hats but with no solution,
I am a computer specialist and I am taking a course about data security and random attacks and it contains a probability part.
June 3rd 2012, 11:15 PM
billobillo

Re: probabiliy of equal cards

Quote:

Originally Posted by bjhopper

Two decks are shuffled. The first is the reference deck and I interpret that the question is what is the P that the second deck will have the exact same order as the first. I would answer 52 factorial is the number of possible events.P= 1/8*10^67

The question is to find the probability for one common card at the same position,and not all common cards