Okay so this friend has a 8, 9, 10 as her options that she pays at.
8: 2,6 9: 6,3 10: 5,5
6,2 3,6 5,5
4,4
4,4
These are the possibilities of rolling these numbers. = 4 possibilities
4/11 (11 because that is the number of possibilities you get for two dice)
that leaves 7/11 possibilities of rolling and not paying!
36% lands on a spot that she pays at and about 64% possibilities of not paying.
Hope this helped!
:)
The Lagrangian,

has critical points where its partial derivatives vanish:





tells us
, so that


Then with
, we get

and
tells us

Then there are two critical points,
. The critical point with the negative
-coordinates gives the maximum value,
.
1 split into two equal parts so the answer is 2