Math CentralQuandaries & Queries


Question from Cori, a parent:

There are 30 marbles in a bag. Twice as many red, as blue, and 1 more green than there are red. What is the probability that when one is pulled out, it will be red?


Are you sure you have correctly reproduced this problem?

Suppose the number of red balls is r, the number of blue balls is b and the number of green balls is g. Then from the problem you know the following.

There are 30 marbles in a bag.
r + b + g = 30

There are twice as many red, as blue.
r = 2b or b = r/2

There is 1 more green than red.
g = r + 1

Substituting the second two facts into the first equation I get

r + r/2 + r + 1 = 30

Multiply both sides by 2 to eliminate the fraction

2r + r + 2r + 2 = 60


5r = 58 and r = 58/5.

Thus the number of red balls is a fraction which is impossible.


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