SOLUTION: If one vase contains 3 red, 4 pink and 5 white roses and another vase has 2 red, 2 pink and 2 white roses, what is probability that one rose chosen from each vase will be the same

Question 584924: If one vase contains 3 red, 4 pink and 5 white roses and another vase has 2 red, 2 pink and 2 white roses, what is probability that one rose chosen from each vase will be the same color? Please explain how to come to the answer. Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 1/3
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