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.

kittykat Jun 21, 2024

#1**+1 **

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! :)

NotThatSmart Jun 21, 2024