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Probability Question

Posted: April 30th, 2017, 8:31 am
by Bob Farmer
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.

Re: Probability Question

Posted: April 30th, 2017, 8:43 am
by HocoPoco
Is this that old "reverse polynomial factored Fibonacci integer" joke?

Re: Probability Question

Posted: April 30th, 2017, 9:59 am
by Jack Shalom
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.

Re: Probability Question

Posted: April 30th, 2017, 10:31 am
by Bob Farmer
Hi Jack:

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

Re: Probability Question

Posted: April 30th, 2017, 11:05 am
by Dave Le Fevre
What Jack said. 1 in 15! , or 5! cubed in 15!, depending on your criteria.

Dave

Re: Probability Question

Posted: April 30th, 2017, 2:28 pm
by McKitterick
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.

Re: Probability Question

Posted: April 30th, 2017, 3:05 pm
by Matthew Field
When I do that 15! bit I always use the out "Off by 1."

Matt Field

Re: Probability Question

Posted: April 30th, 2017, 3:34 pm
by Bob Farmer
Would that be 1,307,674,368,000 in the trillions? My math abilities are sadly deficient.

Is there an online calculator for factorials?

Re: Probability Question

Posted: April 30th, 2017, 4:29 pm
by Brian Douglas
The probability will be 50 - 50. Either it will happen or it won't.


Everything else is horseshoes and hand grenades.

Re: Probability Question

Posted: April 30th, 2017, 5:06 pm
by Steve Bryant
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!

Re: Probability Question

Posted: April 30th, 2017, 6:30 pm
by MagicbyAlfred
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)

Re: Probability Question

Posted: April 30th, 2017, 8:44 pm
by Bob Farmer
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.