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In a garden, there are three blue flowers, three red flowers, three
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06 Apr 2016, 06:03
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76% (01:55) correct 24% (02:10) wrong based on 205 sessions
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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?
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06 Apr 2016, 08:46
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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.
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06 Apr 2016, 10:55
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Bunuel wrote:
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
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
Re: In a garden, there are three blue flowers, three red flowers, three
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12 Apr 2016, 04:50
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R: !!! B: !!! G: !!! P: !!! ways of selecting a color : 4C1 ways of selecting the three flowers within the chosen color: 3C3 ways of selecting three flowers out of 12 : 12C3
Re: In a garden, there are three blue flowers, three red flowers, three
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27 Apr 2016, 01:05
I am a novice in this giving solutions but is too tempted to explain the logic of this one. Overall I have 12 flowers and I need to select just 3 of the same colour out of 12. Let me select blue as my color so the first flower that I pick is blue in color and I can do that in 1 way now the second flower that I need to pick should also be blue in color so I can choose any one out of remaining two blue flowers 2/11 and finally I can choose the last blue flower in 1/10 way So yeah Overall P(z)= 1/55
In a garden, there are three blue flowers, three red flowers, three
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03 Jul 2016, 09:21
Bunuel wrote:
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
{ B B B } , { R R R } , { G G G } , { P P P } = TOTAL 12 FLOWERS
You need 3 flowers , so total no of ways it is possible is \(12c3\) = 220
Now you need one particular colour of flowers from these set...
So, We can have it in 4 ways as the sets the flowers now represents sets as below -
BLUE , RED , GREEN , PINK
\(Probability\) = \(\frac{Favourable \ Outcome}{Total \ Possible \ Outcome}\) => \(\frac{4}{220}\) So, The answer will be (B) _________________
Thanks and Regards
Abhishek....
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Re: In a garden, there are three blue flowers, three red flowers, three
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03 Jul 2016, 10:26
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Bunuel wrote:
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?
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: In a garden, there are three blue flowers, three red flowers, three
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12 Jul 2017, 04:52
Bunuel wrote:
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
Total events = 12 C 3 (i.e. selecting any 3 flowers from total 12 flowers) = 12 x 11 x 10 / 3 / 2 = 2 x 11 x 10
No. of events in which 3 flowers selected will be of same colour = 4 (3 flowers of each colour say RRR, BBB, GGG, PPP)
Re: In a garden, there are three blue flowers, three red flowers, three
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14 Jul 2017, 08:44
Bunuel wrote:
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
Hi Bunuel,
Though I understood the solution, I could not get answer using this approach. Could you help me identify the problem in this approach?
I tried like this - 3B, 3R, 3G, 3P
Now to choose 3 flowers of same colour (3C1*2C1*1C1) * 4/12C3 I am getting 6/55
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28 Nov 2019, 23:38
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