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?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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