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April 21st, 2017, 12:24 PM  #1 
Newbie Joined: Apr 2017 From: Austria Posts: 3 Thanks: 0  Game  probability
Hi, Can someone help mw with a simple probability calculation in a game: What are the chances that a ball fall to a box on the bottom marked from A to R? Ball is dropped from the top and each step has 50% chance to go to left or right 
April 21st, 2017, 11:03 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,408 Thanks: 1459 
How many routes are there to a given box?

April 21st, 2017, 11:38 PM  #3 
Newbie Joined: Apr 2017 From: Austria Posts: 3 Thanks: 0  
April 22nd, 2017, 03:24 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,408 Thanks: 1459 
Try counting the routes, taking into count first 1 row, then two rows, etc., each time treating the count as though other rows don't exist. After you've done this a few times, you'll see how easy it is to count them in total, and it's only slight harder to do the counts for the individual boxes.

April 22nd, 2017, 05:16 AM  #5 
Newbie Joined: Apr 2017 From: Austria Posts: 3 Thanks: 0 
I thought there's a mathematical way to calculate it :\

May 30th, 2017, 06:57 PM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 580 Thanks: 80 
If you add up the 17 values of 16 C x for x from 0 to 16, you get 65,536, which is 2^16, and the bottom row has 16 junctions. I'm not guaranteeing I'm correct, but here are my answers: A: 1/65,536 B: 16/65,536 C: 120/65,536 D: 560/65,536 E: 1,820/65,536 F: 4,368/65,536 G: 8,008/65,536 H: 11,440/65,536 I: 12,870/65,536 J: 11,440/65,536 K: 8,008/65,536 L: 4,368/65,536 M: 1,820/65,536 N: 560/65,536 O: 120/65,536 P: 16/65,536 R: 1/65,536 

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