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# In a garden, there are only red, yellow, and blue flowers.

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In a garden, there are only red, yellow, and blue flowers. [#permalink]  19 Jun 2017, 11:49
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Question Stats:

80% (01:20) correct 19% (01:20) wrong based on 42 sessions

In a garden, there are only red, yellow, and blue flowers. One–third of the flowers are red, and 40 percent are blue. One flower is chosen at random.

 Quantity A Quantity B The probability that the flower chosen is not red The probability the flower chosen is not yellow

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: In a garden, there are only red, yellow, and blue flowers. [#permalink]  16 Sep 2017, 23:42
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The probability that the chosen flower is not red is equal to 1-1/3 = 0.67, i.e. the probability of choosing whatever flower minus the probability of choosing a red flower. The probability that the chosen flower is not yellow is equal to the sum of the probability of the flower being red or blue, i.e. 1/3 + 0.4 = 0.73. Thus the answer is B!
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Re: In a garden, there are only red, yellow, and blue flowers. [#permalink]  22 Sep 2017, 21:56
Carcass wrote:

In a garden, there are only red, yellow, and blue flowers. One–third of the flowers are red, and 40 percent are blue. One flower is chosen at random.

 Quantity A Quantity B The probability that the flower chosen is not red The probability the flower chosen is not yellow

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let take total number of flowers be 90 (Since it is divisible by 3 and 40% x 90 gives an integer , however the total number can be of any value as long as itis divisible by 3 and multiply with 40% gives an integer)

$$\frac{1}{3}$$*90 = 30 Red flowers

and 40% = 90*.4 = 36 blue flowers.

Therefore we have 24 yellow flowers (since 90 - (30+36))

Now The probability that the
flower chosen is not red = $$\frac{60}{90}$$(Since yellow =24 and Blue = 36 ie 24+46 =60)

And The probability the flower chosen is not yellow = $$\frac{66}{90}$$(Since Red =30and Blue = 36 ie 24+36 =66)

Therefore $$\frac{60}{90}$$ < $$\frac{66}{90}$$
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Re: In a garden, there are only red, yellow, and blue flowers. [#permalink]  21 Dec 2018, 23:11
red, yellow, blue flowers
1/3 * total = red
40/100 * total = blue = 2/5 * total
So yellow = total - red - blue = total - 1/3 * total - 4/10 * total = (30-10-12)/ 30 * total = 8/30 *total = 4/15*total

One flower is chosen at random.
A: The probability that the flower chosen is not red: So it can be either blue or yellow:
p(not red) = p(blue + yellow) = p(blue) + p(yellow) = 2/5 * total + 4/15 * total = 2/3 * total

B: The probability that the flower chosen is not yellow. So it can be either blue or red:
p(not yellow) = p(blue + red) = p(blue) + p(red) = 2/5 * total + 1/3 * total = 11/15* total

B is bigger than A. Answer is B.
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Re: In a garden, there are only red, yellow, and blue flowers.   [#permalink] 21 Dec 2018, 23:11
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