Question 584924
There are 3 possible scenarios:


Scenario 1) Both roses are red



P(Both Red) = P(Red)*P(Red) = (3/12)*(2/6) = 6/72 = 1/12


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Scenario 2) Both roses are pink



P(Both Pink) = P(Pink)*P(Pink) = (4/12)*(2/6) = 8/72 = 1/9


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Scenario 2) Both roses are white



P(Both White) = P(White)*P(White) = (5/12)*(2/6) = 10/72 = 5/36



Now add up all the probabilities:


1/12 + 1/9 + 5/36 = 3/36 + 4/36 + 5/36 = (3+4+5)/36 = 12/36 = 1/3



So the probability that one rose chosen from each vase will be the same color is <font color="red">1/3</font>