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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
avatar+18229 
+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.

 Jan 29, 2020
 #2
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+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
avatar+107414 
+1

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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+1

I don't understand, what do you mean by "reduce"?

Guest Jan 30, 2020
 #5
avatar+107414 
+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.

 Jan 31, 2020
 #6
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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
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+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
avatar+107414 
+1

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

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