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# help

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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?

Jan 29, 2020

#1
+18229
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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.

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
#3
+107414
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Hi and thanks Geno.

Geno's answer is not queite right because Geno made a careless error.   The denominators must reduce.

It is without replacement.

Melody  Jan 29, 2020
#4
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I don't understand, what do you mean by "reduce"?

Guest Jan 30, 2020
#5
+107414
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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.

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
#7
+1

I got the correct answer, using your reduce idea, I combined your solution and Geno's solution to get 5/18.

Basically, you only did half of what geno did, and I just added the other half with the reduce thing!

Ans: 5/18

Guest Feb 1, 2020
#8
+107414
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Mine was completely correct.

I did not give you the final answer.   I only gave you P(pop)

You finished it yourself, which is great,  but you should have understood that my answer was purposefully not complete.

Melody  Feb 2, 2020