isn't there something wrong with the data ???
a dice is being rolled 360 times. the dice has 1 red side and 5 black. what is the upper bound to the probability of falling on a red side more than 41 times and less than 59 times ?
X - counts how many times the dice was red, up to 36 times
Y - counts how many times the dice was red up to 50 times
thanks a million !
In rolls the mean number of reds is and the standard deviation is
Now if the range for the number of reds were to this would now be a straight forward application of Chebyscev's inequality (or if the number of throws were rather than ).
I don't think that the 1-sided Chebyshev inequality will work here, so you may have a type.