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Alphonse and Beauregard each roll one fair cubical die, nubmered from 1 through 6.  Find the probability that Alphonse rolls a higher number than Beauregard.

 Dec 10, 2019
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There are 36 possible combinations of rolls

if B rolls a

1   there are 5 higher rolls that A could roll

2                   4

3                   3

4                   2

5                   1        5 + 4 +3 + 2 + 1     15 out of 36 combinations with A> B      15/36= 5/12

 

(as an aside: there will be 15 rolls where  A < B   and  6 will be ties    15 + 15 + 6 = 36 possible rolls)

 Dec 10, 2019
edited by ElectricPavlov  Dec 10, 2019

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