My wife is going back to college for a Master's degree and is taking some probability courses. I took a lot of Probability and statistics back in school, but I haven't used any of it in 5 years. She has a question, and I want to help, but I think I'm missing something.
[Question]
Helen and Adiana are playing cards. They each shuffle a standard deck of cards thoroughly, demonstrating their fanciest casino-style moves. What is the probability that both decks are in the EXACT same order after all that shuffling?
My current answers are 1/(52!*52!) or 52/(52!*52!), but I feel I am doing something wrong. This is a pretty basic course. So far they have only used the basic permutation formula and some tree diagrams. I don't they have gotten into conditional probabilities yet.
One final thought... I tried to work backwards and figure out what the probability of them *NOT* matching was and then subract it from one. I don't think that worked so well for me.
If Helen has a probability of 1/52! of getting a specific order (any order), then Adiana has a probability of (52!-1)/52! of getting anything EXCEPT the order that helen got.
if (52!-1)/52! is anything EXCEPT the order that Helen got, then 1 - [(52!-1)/52!] is the exact order that Helen got.
Which reduces to --> 1/52! and that can't be right.
It doesn't matter what the first deck is. The second deck has to match it.