How to determine the sign of the result obtained from (p_1-p_2)?

Questions
1

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p1 = (1 - (1 - p)^3) q^3 // Expand
p2 = (1 - (1 - q)^3) p^3 // Expand
p1 - p2 // Simplify // Factor
Simplify[Sign[p1 - p2], 0 < p < q]
2

You can solve the inequalities:

Reduce[p1 - p2 > 0 && 0 < p < q, {p, q}]
Reduce[p1 - p2 == 0 && 0 < p < q, {p, q}]
Reduce[p1 - p2 < 0 && 0 < p < q, {p, q}]