How to solve the problem according to theory. probabilities?

Question

Probability theory

Urn contains A white and B black balls (A>=2;B>=2). Two balls are taken out of the urn at the same time. Which event is more likely: 1 = {balls of the same color}, 2={balls of different colors}

Answer 1

P _od \u003d (A / (A + B)) * ((A-1) / (A + B-1)) + (B / (A + B)) * ((B-1) / (A + B -1)) \u003d (A ² -A + B ² -B) / ((A + B) * (A + B-1))
P _diff \u003d (A / (A + B)) * (B / (A +B-1))+(B/(A+B))*(A/(A+B-1)) = 2AB//((A+B)*(A+B-1))