Go Premium for a chance to win a PS4. Enter to Win

x
?
Solved

Basic Probability Question

Posted on 2006-06-29
3
Medium Priority
?
285 Views
Last Modified: 2013-11-13

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.
0
Comment
Question by:_TAD_
  • 2
3 Comments
 
LVL 27

Accepted Solution

by:
d-glitch earned 2000 total points
ID: 17012499
It is just 1/(52!)

It doesn't matter what the first deck is.  The second deck has to match it.
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 17012530
The probability of the first card matching in each deck is 1/52.

Given that the first card did match, the probability of the second card matching is 1/51.

And so on...
0
 
LVL 22

Author Comment

by:_TAD_
ID: 17012719

Gosh... and to think all this time I thought I forgot everything I learned in college.


I came up with the 1/52! in the first two minutes, and then spent the next 40 min thinking I was wrong (and trying to figure out the "right" answer).


Thanks for the clarification!
0

Featured Post

Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
Dependencies in Software Design In software development, the idea of dependencies (http://en.wikipedia.org/wiki/Coupling_%28computer_programming%29) is an issue of some importance. This article seeks to explain what dependencies are and where they …
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

972 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question