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Topic: Entertaining probability question
Replies: 10   Last Post: Jun 29, 2014 4:09 PM

 Messages: [ Previous | Next ]
 Mike Terry Posts: 730 Registered: 12/6/04
Re: Entertaining probability question
Posted: Jun 29, 2014 2:35 PM

"Port563" <reader80@eternal-september.org> wrote in message
news:lopjgm\$ne7\$1@dont-email.me...
> "Mike Terry" <news.dead.person.stones@darjeeling.plus.com> wrote...
> > "Michael Press" <rubrum@pacbell.net> wrote in message
> > news:rubrum-F6BA62.21323027062014@news.albasani.net...

> >> In article <lojgns\$bto\$1@dont-email.me>,
> >> "Port563" <reader80@eternal-september.org> wrote:
> >>

> >> > A standard deck of 52 cards is thoroughly shuffled.
> >> >
> >> > What is the probability that exactly two aces** occupy adjacent

> > positions
> >> > within the deck?
> >> >
> >> >
> >> > "Hint": Some may wish to consider the adjacent aces as if they were

one
> >> > card.
> >> >
> >> > (-:
> >> >
> >> > While I think the above is unambiguous, for the avoidance of doubt it

> > means
> >> > that none of these orderings qualify:
> >> > ...xxxxxAxxxAxxxxxxAxxxxxAxxxx...
> >> > ...xxxxxxxxAAxxxxxxxxxxxAAxxxx...
> >> > ...xxxxxxxxAAAxxxxxxxxxxAxxxxx...
> >> > ...xxxxxxxxAAAAxxxxxxxxxxxxxxx...

> >>
> >> Number of ways of putting 4 distinguishable aces in 3 distinguishable

> > places
> >> times the number of ways of selecting 3 from 49 without replacement
> >> divided by 52!.

> >
> > I don't think I can be looking at this right - if you select 3 from 49,
> > some
> > of the 3 could be adjacent, which would upset the calculation it seems

to
> > me...
>
>
> Think "gaps" or "holes".
>
> Adjacency is not possible to represent (and therefore to occur) in this
> model, as apparently adjacent gaps would still have a non-ace between
> them.
>

Thanks, I wasn't thinking "holes"! :)

Date Subject Author
6/27/14 Port563
6/27/14 quasi
6/27/14 Peter Percival
6/28/14 Michael Press
6/28/14 quasi
6/28/14 Michael Press
6/28/14 Mike Terry
6/29/14 Port563
6/29/14 Mike Terry
6/29/14 Port563
6/29/14 Bart Goddard