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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.

 Mar 31, 2024
 #1
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Probability of purple orangle purple:

\(\frac{2}{5}*\frac{3}{4}*\frac{1}{3}=\frac{1}{10}\)

Probability of orange purple orange:

\(\frac{3}{5}*\frac{1}{2}*\frac{2}{3}=\frac{1}{5}\)

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

The probability that the balls alternate is 3/10.

 Apr 1, 2024

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