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.

Re: probabiliy of equal cards

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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?

Re: probabiliy of equal cards

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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.

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 $\displaystyle p$ is the probability of **not having any card in its correct place** then $\displaystyle 1-p$ is the probability of at least one card in its correct place.

Do you know about derangements ?

Re: probabiliy of equal cards

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Originally Posted by

**Plato** That is correct. So if $\displaystyle p$ is the probability of

**not having any card in its correct place** then $\displaystyle 1-p$ 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?

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?

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

Re: probabiliy of equal cards

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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!

Re: probabiliy of equal cards

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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.

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