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A flower arrangement consists of 30 roses, each of which is either whi

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A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 03 Jul 2018, 23:08
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A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?

A. 5
B. 10
C. 15
D. 20
E. 25

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Re: A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 03 Jul 2018, 23:14
Ans: D
given that total roses =30
P(w)=2P(r)
We know there are only white or red roses so P(w)+P(r)=1
so 3P(r)=1 ; P(r) =1/3 this mean P(w) = 2/3 = 20/30 where 30 is the total outcome and 20 will be the favourable outcomes.
no. of white roses = 20

Bunuel wrote:
A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?

A. 5
B. 10
C. 15
D. 20
E. 25

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Re: A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 05 Jul 2018, 03:01
3

Solution



Given:
    • Total number of roses in the flower arrangement = 30
    • Each rose is either white or red in color
    • A rose is randomly selected from the arrangement
    • The probability that the selected rose will be white = 2 * the probability that the selected rose will be red

To find:
    • Number of white roses in the arrangement

Approach and Working:
    • Assume the probability of the selected rose will be white as P(w), and the probability of the selected rose will be red as P(r)
    • P(r) + P(w) = 1, and ……………………………………. (1)
    • Also given, P(w) = 2 * P(r) …………………………... (2)
    • From (1) and (2), we get
      o P(r) = \(\frac{1}{3}\) and P(w) = \(\frac{2}{3}\)
    • P(w) = total number of WHITE roses/ total number of roses
    • Therefore, the number of white roses in the arrangement = \(\frac{2}{3} *\) total number of roses
    • Thus, number of white roses = \(\frac{2}{3} * 30\) = 20

Hence, the correct answer is option D.

Answer: D
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Re: A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 11 Jul 2018, 07:53
For the probability of having a white rose to be twice the probability of picking a red one, we need twice as many white roses as red, or 2 parts of white roses for each part of red roses.

To meet this ratio 2:1 in a total of 30 roses we need 20 white roses and 10 red.

Answer D
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A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 20 Jul 2018, 12:46
EgmatQuantExpert wrote:

Solution



Given:
    • Total number of roses in the flower arrangement = 30
    • Each rose is either white or red in color
    • A rose is randomly selected from the arrangement
    • The probability that the selected rose will be white = 2 * the probability that the selected rose will be red

To find:
    • Number of white roses in the arrangement

Approach and Working:
    • Assume the probability of the selected rose will be white as P(w), and the probability of the selected rose will be red as P(r)
    • P(r) + P(w) = 1, and ……………………………………. (1)
    • Also given, P(w) = 2 * P(r) …………………………... (2)
    • From (1) and (2), we get
      o P(r) = \(\frac{1}{3}\) and P(w) = \(\frac{2}{3}\)

    • P(w) = total number of WHITE roses/ total number of roses
    • Therefore, the number of white roses in the arrangement = \(\frac{2}{3} *\) total number of roses
    • Thus, number of white roses = \(\frac{2}{3} * 30\) = 20

Hence, the correct answer is option D.

Answer: D


I get up to the point where the 1/3 and 2/3 come in... am I missing something obvious? Because that makes zero sense to me and it is driving me crazy trying to figure it out. Where did the 1/3 come in?
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Re: A flower arrangement consists of 30 roses, each of which is either whi  [#permalink]

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New post 20 Jul 2018, 13:20
1
aanjumz92 wrote:
EgmatQuantExpert wrote:

Solution



Given:
    • Total number of roses in the flower arrangement = 30
    • Each rose is either white or red in color
    • A rose is randomly selected from the arrangement
    • The probability that the selected rose will be white = 2 * the probability that the selected rose will be red

To find:
    • Number of white roses in the arrangement

Approach and Working:
    • Assume the probability of the selected rose will be white as P(w), and the probability of the selected rose will be red as P(r)
    • P(r) + P(w) = 1, and ……………………………………. (1)
    • Also given, P(w) = 2 * P(r) …………………………... (2)
    • From (1) and (2), we get
      o P(r) = \(\frac{1}{3}\) and P(w) = \(\frac{2}{3}\)

    • P(w) = total number of WHITE roses/ total number of roses
    • Therefore, the number of white roses in the arrangement = \(\frac{2}{3} *\) total number of roses
    • Thus, number of white roses = \(\frac{2}{3} * 30\) = 20

Hence, the correct answer is option D.

Answer: D


I get up to the point where the 1/3 and 2/3 come in... am I missing something obvious? Because that makes zero sense to me and it is driving me crazy trying to figure it out. Where did the 1/3 come in?
Consider the whole question more simply, this is a simple case of probability so the probability will be directly proportional to the number of items (that is flowers here).
So when they say that the probability of getting white is double than that of getting red, it simply means that is x is the number of red flowers, then 2x is the number of white flowers in the setup.
After this,
x+2x=30
x=10
Therefore number of white flowers is 2x ie 20

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Re: A flower arrangement consists of 30 roses, each of which is either whi &nbs [#permalink] 20 Jul 2018, 13:20
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