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 April 21st, 2017, 11:24 AM #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, 10:03 PM #2 Global Moderator   Joined: Dec 2006 Posts: 18,954 Thanks: 1601 How many routes are there to a given box?
April 21st, 2017, 10:38 PM   #3
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Joined: Apr 2017
From: Austria

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Quote:
 Originally Posted by skipjack How many routes are there to a given box?
Hmm...i wouldn't know

I draw an example when ball is dropped differently but having the same result

 April 22nd, 2017, 02:24 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,954 Thanks: 1601 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, 04:16 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, 05:57 PM #6 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 600 Thanks: 82 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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