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      Question

      A shop has a total of 30 bottles, consisting of x red

      bottles and some blue and green bottles. The ratio of blue to green bottles is 3:2, and the average number of blue and green bottles combined is x. If two bottles are randomly selected from the stock, what is the probability that at least one of them is a green bottle?
      A 52/217 Correct Answer Incorrect Answer
      B 68/145 Correct Answer Incorrect Answer
      C 68/155 Correct Answer Incorrect Answer
      D 41/263 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      The total number of bottles in a shop=30 The number of green bottles in a shop=2a The number of blue bottles in a shop=3a (2a+3a)=2x 2x+x=30 x=10 The number of red bottles in a shop=10 The number of green and blue bottles in a shop=30-10=20 The number of blue bottles in a shop=20*3/5=12 The number of green bottles in a shop=20-12=8 Required probability= (8C1*22C1+8C2)/30C2 = (176+28)/ (15*29) =68/145

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