P(1st brown AND 2nd brown) OR P(1st white AND 2nd white) =
and since AND is a clue to multiply and OR is a clue to add,
P(1st brown)×P(2nd brown) + P(1st white)×P(2nd white) =
P(1st brown) = 5/9
P(2nd brown, when 1st was brown) = 4/8
P(1st white) = 4/9
P(2nd white, when 1st was white) = 3/8
P(1st brown)×P(2nd brown) + P(1st white)×P(2nd white) =
(5/9)(4/8) + (4/9)(3/8)
20/72 + 12/72
32/72
4/9