First out is first out

A bag contains 5 black and 20 blue marbles.

They are to be drawn one at a time until all of one color has been exhausted.

What is the probability that the color of the first marble drawn is the same as the first color exhausted?

1 5 \frac{1}{5} 1 4 \frac{1}{4} 1 3 \frac{1}{3} 1 2 \frac{1}{2} 3 4 \frac{3}{4}

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1 solution

Jeremy Galvagni
May 9, 2018

Consider drawing all 25 marbles instead of stopping when one color is exhausted. All that really matters is the first and last are different colors:

2 5 25 20 24 = 1 3 2*\frac{5}{25}*\frac{20}{24}=\boxed{\frac{1}{3}}

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