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04 Jul 2018, 00:08
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D
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Difficulty:
5%
(low)
Question Stats:
89% (01:00) correct
11%
(01:16)
wrong
based on 1195
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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
A. 5
B. 10
C. 15
D. 20
E. 25
Ans: D
Easiest way:
P(w) = 2P(r)
because there are only red and white roses that means total of 30 roses are divided between White and Red in 2:1 (only then P(w) can be twice the P(r)
so White roses = 2 * 30/3 = 20
Another way to say the same
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
Easiest way:
P(w) = 2P(r)
because there are only red and white roses that means total of 30 roses are divided between White and Red in 2:1 (only then P(w) can be twice the P(r)
so White roses = 2 * 30/3 = 20
Another way to say the same
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
05 Jul 2018, 04:01
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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) = \(\frac{2}{3}\)
• 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
