My Math Forum Probability Of Consecutive Numbers When Numbers Are Paired

 January 26th, 2015, 05:59 AM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 631 Thanks: 85 Probability Of Consecutive Numbers When Numbers Are Paired The numbers 1 to 20 are randomly made into ten pairs with every number used once. What is the probability that at least four of the pairs will have consecutive numbers? Note that most numbers can be consecutive with a number 1 higher or 1 lower but 1 and 20 are exceptions. I did 10 random number simulations and the most pairs with consecutive numbers I got was 2 pairs in one simulation. It only happened 9 times in the 10 simulations combined. Therefore I'm expecting a very low probability.
 January 26th, 2015, 06:32 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,572 Thanks: 2568 Math Focus: Mainly analysis and algebra How about looking at this method of generating arrangements? Let case $(n,p)$ be the problem of getting $p$ or more pairs out of $n$ consecutive numbers placed in $n$ positions. Case $(n,p)=(20,4)$: Place the 1 in one of the 20 positions. Now place the 2 in one of the 19 remaining positions. If it is not paired with the 1, you can no longer pair the 1, so we are now reduced to the case $(19,4)$ (with the first number already placed). (Note that this case has non-pairable places, but I'm not sure that it matters. If it is paired with the 1, we have one pair and we are reduced to the case $(18,3)$.

 Tags consecutive, numbers, paired, probability

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post EvanJ Advanced Statistics 7 March 8th, 2014 09:33 PM johnr Number Theory 5 March 5th, 2014 12:03 PM ganeshsrivatsav Number Theory 2 November 15th, 2013 09:43 PM daigo Algebra 1 May 18th, 2012 03:59 PM coax Number Theory 1 July 24th, 2009 06:36 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top