For roots to be real,
$ b^2 - 4ac >= 0 $
the following values of {b,a,c} are possible,
{2,1,1}
{3,1,1} {3,1,2} {3,2,1}
{4,1,1} {4,1,2} {4,2,1} {4,2,2} {4,3,1} {4,13,}
{5,1,1} {5,1,2} {5,2,1} {5,2,2} {5,3,2} {5,2,3} {5,3,1} {5,1,3}
{6,1,1} {6,1,2} {6,2,1} {6,2,2} {6,3,1} {6,1,3} {6,3,3} {6,3,2} {6,2,3}
These are 27 cases.
While the total cases possible for the values of a, b, c are 6*6*6 hence probability equals $\frac{27}{216}$ = $0.125$
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For the roots to be complex, 60 - 27 = 33 cases are possible, probability equals $\frac{3}{216}$ = $0.152$
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For roots to be equal, discriminant
$ b^2 - 4ac = 0 $
which is possible for the following values of {b,a,c} only {6,3,3}, {4,2,2}, {2,1,1}, probability equals
$\frac{3}{216}$ = $0.0138$