Probability Question

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Bob Farmer
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Probability Question

Postby Bob Farmer » April 30th, 2017, 8:31 am

15 cards can be arranged in 307,674,368,000 ways (factorial 15, 15 X 14 X 13, etc.).

What is the probability that if 15 cards consisting of a royal flush in spades, a royal flush in diamonds and the 5, 6, 7, 8, 9 in hearts will, after a random shuffle, end up in this order from top to bottom as the cards are held face down:

5, 6, 7, 8, 9 of hearts, 10, J, Q, K, A of spades, 10, J, Q, K, A of diamonds.

HocoPoco
Posts: 32
Joined: March 30th, 2008, 6:36 pm

Re: Probability Question

Postby HocoPoco » April 30th, 2017, 8:43 am

Is this that old "reverse polynomial factored Fibonacci integer" joke?

Jack Shalom
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Location: Brooklyn NY

Re: Probability Question

Postby Jack Shalom » April 30th, 2017, 9:59 am

If you want that exact order then of course 1 out of 15 factorial.

But if you don't care about the order within the suits, but do care about all the cards of one suit being together and in that particular suit order, then your probability increases to 120x 120x 120 out of 15 factorial.

Bob Farmer
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Joined: January 17th, 2008, 12:00 pm
Location: Short card above selection.

Re: Probability Question

Postby Bob Farmer » April 30th, 2017, 10:31 am

Hi Jack:

Thank you. Please send me an email to trickmail@cogeco.ca.

Dave Le Fevre
Posts: 36
Joined: December 24th, 2015, 10:29 am
Favorite Magician: Paul Megram

Re: Probability Question

Postby Dave Le Fevre » April 30th, 2017, 11:05 am

What Jack said. 1 in 15! , or 5! cubed in 15!, depending on your criteria.

Dave

McKitterick
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Joined: July 26th, 2008, 10:07 pm

Re: Probability Question

Postby McKitterick » April 30th, 2017, 2:28 pm

Point of order: It may have been a typo in the original post but for the sake of accuracy in calculations with respect to this probability question, 15! actually works out to equal 1,307,674,368,000.

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Matthew Field
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Favorite Magician: Slydini
Location: Hastings, England, UK

Re: Probability Question

Postby Matthew Field » April 30th, 2017, 3:05 pm

When I do that 15! bit I always use the out "Off by 1."

Matt Field

Bob Farmer
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Joined: January 17th, 2008, 12:00 pm
Location: Short card above selection.

Re: Probability Question

Postby Bob Farmer » April 30th, 2017, 3:34 pm

Would that be 1,307,674,368,000 in the trillions? My math abilities are sadly deficient.

Is there an online calculator for factorials?

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Brian Douglas
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Joined: November 19th, 2016, 10:34 am
Favorite Magician: Salguod Nairb
Location: Middle East
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Re: Probability Question

Postby Brian Douglas » April 30th, 2017, 4:29 pm

The probability will be 50 - 50. Either it will happen or it won't.


Everything else is horseshoes and hand grenades.

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Steve Bryant
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Favorite Magician: Ballantine
Location: Bloomington IN
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Re: Probability Question

Postby Steve Bryant » April 30th, 2017, 5:06 pm

Re "Is there an online calculator for factorials?"

go to google and type What is 15!

The answer pops up in an online calculator. This is neat!

MagicbyAlfred
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Joined: June 7th, 2015, 12:48 pm
Favorite Magician: Bill Malone
Location: Santa Rosa, California

Re: Probability Question

Postby MagicbyAlfred » April 30th, 2017, 6:30 pm

Bob wrote:"1,307,674,368,000 in the trillions?"

Yes, one trillion, 307 billion, 674 million, 368 thousand

Easy way to figure is to first segregate the number on the right that is in the hundreds of thousands (in this case 368,000). Then working your way LEFT, the next three-digit number is in the millions (here 674 million) then the next three-digit number is in the billions (here 307 billion) then finally the next number to the left (irrespective of the number of digits) is in the trillions (here one trillion)

Bob Farmer
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Joined: January 17th, 2008, 12:00 pm
Location: Short card above selection.

Re: Probability Question

Postby Bob Farmer » April 30th, 2017, 8:44 pm

Wow. That's great. I have a card trick that has once chance in one trillion, 307 billion, 674 million, 368 thousand of being successful--however, the magician triumphs and is successful. It will be in a manuscript I'm working on entitled, "Tarodiction." This will include an extensive development of what, up to now, has been a principle that has seen very little, if any use, for magic. Will advise when available. If you are interested in cards, the manuscript will be invaluable.


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