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A box contains some green marbles and exactly four red marbles. The probability of selecting a red marble is x%. If the number of green marbles is doubled, the probability of selecting one of the four red marbles from the box is (x − 15)%. How many green marbles are in the box before the number of green marbles is doubled?

 May 29, 2020
 #1
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At first:

     Number of red marbles:  R

     Number of green marbles:  4

     Probability of drawing a red marble:  R / (R + 4)  =  x

 

After doubling the number of green marbles:

    Number of red marbles:  R

    Number of greeen marbles:  8

    Probability of drawing a red marble:  R / (R + 8)  =  x - 0.15

      ---   solving this equation for x:         R / (R + 8) + 0.15  =  x

 

Setting the two equations equal to each other: 

         R / (R + 4)  =  R / (R + 8) + 0.15 

 

Multiplying all terms by  (R + 4) · (R + 8)

          R · (R + 8)  =  R · (R + 4) + (0.15) · (R + 8) · (R + 4)

Multipling out:

          R2 + 8R  =  R2 + 4R + 0.15(R2 + 12R + 32)

          R2 + 8R  =  R2 + 4R + 0.15R2 + 1.8R + 4.8

Simplifying:

                    0  =  0.15R2 - 2.2R + 4.8

Multiplying by 100:

                    0  =  15R2 - 220R + 480

Dividing by 5:

                    0  =  3R2 - 44R + 96

Factoring:

                    0  =  (3R + 8)(R - 12)

 

Answers:  either  -8/3 (impossible)  or  12

 May 29, 2020

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