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Probability calculation in a simple game Probability calculation in a simple game

04-22-2017 , 09:06 AM
Hi guys!

I know it's poker forum but still I hope someone will help me with a probability calculation in a simple game:



What are the chances that a ball fall to a box on the bottom marked from A to R?
How many combinations there is?

Ball is dropped from the top and each step have 50% chance to go to left or right

Example for two balls with same result:
Probability calculation in a simple game Quote
04-22-2017 , 12:48 PM
Look up Pascal's triangle.
Probability calculation in a simple game Quote
04-23-2017 , 02:10 AM
Thank's for tip

So this is exactly the same as my picture above:



If I get it right...the number of all combinations is to sum lowest line (1+16+120+560...)= 65536 total combinations

For a ball fall into the middle line (12870) it has 19,63806% chance or 1:5.09215
Is this correct?
Probability calculation in a simple game Quote
04-23-2017 , 01:27 PM
Quote:
Originally Posted by Lampinjon


1) If I get it right...the number of all combinations is to sum lowest line (1+16+120+560...)= 65536 total combinations

2) For a ball fall into the middle line (12870) it has 19,63806% chance or 1:5.09215
Is this correct?
Yes but instead of creating a triangle,

1) The sum of row n is 2^n, the total number of combinations of n trials with 50/50 occurrence of yes-no, heads-tails, left-right, etc.

2) This can be gotten directly using the binomial distribution.
Probability calculation in a simple game Quote
04-25-2017 , 09:49 AM
Quote:
Originally Posted by statmanhal
2) This can be gotten directly using the binomial distribution.
And since these are 50/50 events, that amounts to using combinations.

combin(n, r) / 2^n

How many ways are there to pick 8 objects from a set of 16?
Probability calculation in a simple game Quote
04-26-2017 , 10:43 PM
Thats a Galton box.

The probability of landing in the kth box follows a binomial probability mass function.
Probability calculation in a simple game Quote

      
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