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06 Apr 2016, 07:03
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B
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In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16
A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16
06 Apr 2016, 09:46
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Total number of ways to pick 3 flowers out of 12 = 12c3
\(12c3 = \frac{12!}{9!*3!} = 220\)
Total number of favorable outcomes = 4
(Only 3 flowers per colour, so there is only one way all three flowers of any particular colour can be chosen. 4 colours mean 4 favorable outcomes)
Probability = \(\frac{4}{220} = \frac{1}{55}\)
Answer: B
Alternatively, if you like the slot method, the first flower can be chosen at random, it doesn't matter. The second flower must be the same colour as the first - probability = 2/11. The third flower must be the same colour as the first two - probability = 1/10.
\(\frac{2}{11}*\frac{1}{10} = \frac{1}{55}\)
\(12c3 = \frac{12!}{9!*3!} = 220\)
Total number of favorable outcomes = 4
(Only 3 flowers per colour, so there is only one way all three flowers of any particular colour can be chosen. 4 colours mean 4 favorable outcomes)
Probability = \(\frac{4}{220} = \frac{1}{55}\)
Answer: B
Alternatively, if you like the slot method, the first flower can be chosen at random, it doesn't matter. The second flower must be the same colour as the first - probability = 2/11. The third flower must be the same colour as the first two - probability = 1/10.
\(\frac{2}{11}*\frac{1}{10} = \frac{1}{55}\)
Updated on: 12 Oct 2021, 10:59
Originally posted by BrentGMATPrepNow on 06 Apr 2016, 11:55.
Last edited by BrentGMATPrepNow on 12 Oct 2021, 10:59, edited 1 time in total.
Last edited by BrentGMATPrepNow on 12 Oct 2021, 10:59, edited 1 time in total.
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Bunuel
P(all the same color) = P(1st flower is ANY color AND 2nd flower is same as first AND 3rd flower is also the same color)
= P(1st flower is ANY color) x P(2nd flower is same as 1st) AND P(3rd flower is the same color)
= 1 x 2/11 x 1/10
= 1/55
Answer: B
