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.
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?
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