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.

 Jun 21, 2024

There are two seperate cases we need to consider. 


First off, we have orange, purple, orange. 

The probability of this is \(\frac{3}{5}*\frac{2}{4}*\frac{2}{3} = 1/5\)


The other case is when we have purple, orange, purple. 

The probability of this is \(\frac{2}{5}*\frac{3}{4}*\frac{1}{3} = 1/10\)


Adding these two up, we get

\(\frac{1}{5}+\frac{1}{10} = \frac{2}{10}+\frac{1}{10}=\frac{3}{10}\)


So our answer is 3/10 or 30%. 


Thanks! :)

 Jun 21, 2024

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