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by C » Tue Apr 13, 2010 11:00 pm
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at random in a bouquet. However, the customer calls and says she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?

OA is [spoiler]13/18[/spoiler]

Source is MGMAT Word Translations, answer choices were not given. I did not understand the explanation, can someone please solve and explain?

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by thephoenix » Tue Apr 13, 2010 11:58 pm
What is the probability that the florist does not have to change the bouquet? ---->MEANS THE florist has kpt two diff flowers
so we need to find the probability of keeping two diff flowers in the bouquet
which is same as 1- probability of keeping two same flowers in the bouquet
probability of keeping two same flowers in the bouquet=(2C2+3C2+4C2)/9C2=10/36
REQD PROBABILITY=1-10/36=26/36=13/18
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by neoreaves » Wed Apr 14, 2010 12:17 am
2A, 3B, 4P

Total = 9

Probability of picking both A = 2/9 x 1/8
Probability of picking both B = 3/9 x 2/8
Probability of picking both P = 4/9 x 3/8

Probability of picking same = 2/9 x 1/8 + 3/9 x 2/8 + 4/9 x 3/8 = 20/72

Probability she wont have to change the flowers = Probability of not picking same = 1 - 20/72 = 13/18
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