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Raina places the following balls into a bag.  She then 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 3 orange balls and 2 purple balls.

 May 9, 2024
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\(\quad\text{Required probability}\\ = \dfrac35 \cdot \dfrac24 \cdot \dfrac23 + \dfrac25 \cdot \dfrac34 \cdot \dfrac13\\ =\dfrac3{10}\)

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 May 10, 2024

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