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Raina places the following balls into a bag.  She draws three balls out of the bag, one at a time, without replacement.  What is the probability that the colors of the balls alternate?

 

There are 6 orange balls and 6 purple balls.

 Feb 14, 2024
 #1
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The first ball doesn't matter, because no matter what ball they draw, the only condition is the next one needs to be the opposite color

After Rainas draws the first one, there is 11 balls, 6 of the opposite color, so the probability the next ball is the opposite color is \(\frac{6}{11}\). If this happens, there is now 10 balls, 5 of each color, so now there is a \(\frac{1}{2}\) chance of drawing a different colored ball.

So the probability is \(\frac{6}{11}*\frac{1}{2}=\frac{3}{11}\).

 Feb 15, 2024

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