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In a bag of balloons, the ratio of red balloons to other colours is 1:

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Bunuel
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In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink] New post   01 Mar 2021, 04:43
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In a bag of balloons, the ratio of red balloons to other colors is 1:5, if 3 balloons are selected from the bag at random, what is the probability that exactly one balloon is red ?


(A) 91/216
(B) 25/72
(C) 71/216
(D) 61/216
(E) 59/216
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B
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Re: In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink] New post   01 Mar 2021, 05:54
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Probability of selecting a red balloon = 1/6

Probability of not selecting a red balloon = 1 - 1/6 = 5/6

Probability that exactly 1 balloon is red.

Assuming the first pick is red and the other 2 are other colors, then the probability = 1/6 * 5/6 * 5/6 = 25/216

There are 3 ways of picking i.e RCC, CRC and CCR.

Therefore the required probability = 3 * 25/216 = 75/216 = 25/72


Option B

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Re: In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink] New post   01 Mar 2021, 08:21
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Bunuel wrote:
In a bag of balloons, the ratio of red balloons to other colors is 1:5, if 3 balloons are selected from the bag at random, what is the probability that exactly one balloon is red ?


(A) 91/216
(B) 25/72
(C) 71/216
(D) 61/216
(E) 59/216


We need to select one red balloon and 2 of the other color.

Prob(Red first, other colors second and third) = \(\frac{1}{6}*\frac{5}{6}*\frac{5}{6} = \frac{25}{216}\)

However, we can have the red balloon come first, second, or third. So multiply the probability above by 3 to account for that, we would have \(\frac{25}{72}\) as our answer.

Ans: B
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Re: In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink] New post   01 Mar 2021, 08:32
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Total balloons: 6

Red: 1
Other colors: 5

P(R): \(\frac{1}{6}\)

P(other colors): \(\frac{5}{6}\)

Ways to select 3 balloons: 3 [R, O, O or O, R, O, O, O, R]

P(exactly one red) : \(\frac{1}{6}\) * \(\frac{5}{6}\) * \(\frac{5}{6}\) * 3 = \(\frac{25}{72}\)

Answer B
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Re: In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink] New post   14 Oct 2023, 11:53
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Re: In a bag of balloons, the ratio of red balloons to other colours is 1: [#permalink]
14 Oct 2023, 11:53
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