A bag contains 4 orange balls and 5 purple balls. Raina draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?

Guest Jan 29, 2020

#1**+1 **

This could be done in two ways: orange - purple - orange or purple - orange - purple

orange - purple - orange = (4/9) x (5/9) x (3/9) = 60/729

purple - orange - purple = (5/9) x (4/9) x (4/9) = 80/729

To find the final probability, add these two probabilities together.

geno3141 Jan 29, 2020

#2**+1 **

I tried that but it didn't work, I don't know what could have gone wrong, it looks like the right answer to me.

Guest Jan 29, 2020

#5**+1 **

A bag contains 4 orange balls and 5 purple balls. Raina draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?

e.g.

P(pop) = \(\frac{5}{9}*\frac{4}{8}*\frac{4}{7}\)

The numbers get smaller as the balls are removed.

For instance if there are 4 orange, and 5 purple balls and you remove a purple one

then for the next drawer there is only 4 orange, 4 purple and 8 altogether.

Melody Jan 31, 2020

#6**0 **

So the answer is 5/9 * 4/8 * 4/7? Which is 10/63 which is wrong. Maybe because in geno's solution, he added the probabilities together, but in yours you didnt?

Guest Feb 1, 2020