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April 21st, 2017, 12:24 PM   #1
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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
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April 21st, 2017, 11:03 PM   #2
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How many routes are there to a given box?
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April 21st, 2017, 11:38 PM   #3
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Quote:
Originally Posted by skipjack View Post
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
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April 22nd, 2017, 03:24 AM   #4
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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.
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April 22nd, 2017, 05:16 AM   #5
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I thought there's a mathematical way to calculate it :\
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May 30th, 2017, 06:57 PM   #6
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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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