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A certain stationary store arranges notebooks on display such that eac

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A certain stationary store arranges notebooks on display such that eac  [#permalink]

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New post 07 Feb 2020, 06:46
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A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks– white,yellow, orange, green, red, blue, and purple— are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2

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Re: A certain stationary store arranges notebooks on display such that eac  [#permalink]

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New post 08 Feb 2020, 23:44
Bunuel wrote:
A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks– white,yellow, orange, green, red, blue, and purple— are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2


Solution:
    • There is a total of \(7\) different colors.
      o They are arranged in a consecutive repeating pattern.
         The color of every 8th notebook is the same.
    • Now, 8 consecutive notebooks are selected.
      o This means there are exactly two notebooks of the same color. (For example, PWTOGRBP)
      o There are seven different possibilities for selecting two notebooks of the same color. (Total cases)
    • If the first notebook is purple, then the last notebook will also be purple, this is the only favorable case.
      o Probability of selecting two purple notebooks = \(\frac{1}{7}\)
Hence, the correct answer is Option C.
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Re: A certain stationary store arranges notebooks on display such that eac   [#permalink] 08 Feb 2020, 23:44
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