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A box contains 4 white b***s and 4 black b***s. I draw them out of the box, one at a time. What is the probability that all of my draws alternate colors?

 May 5, 2015

Best Answer 

 #1
avatar+130466 
+16

 

 

Mellie.....others on this site  (Melody, for instance) are better at these than I am.....but I'll venture an answer

I see all the white b***s as being indistiguishable  from each other....and the same with the black b***s

So.....this amounts to the same thing as the number of identifiable "words" we could form with, say, 4 e's and 4 h's'

And this is given by    8!  / (4! * 4!)  =  70

There are only 2 ways to draw alternate colors  .... BWBWBW.......etc.    or   WBWBWB......etc.

So.....the probability of alternating colors on the draws is just  2 / 70   or 1 / 35

If this isn't correct......maybe wait until Melody comes on later.....

 

  

 May 6, 2015
 #1
avatar+130466 
+16
Best Answer

 

 

Mellie.....others on this site  (Melody, for instance) are better at these than I am.....but I'll venture an answer

I see all the white b***s as being indistiguishable  from each other....and the same with the black b***s

So.....this amounts to the same thing as the number of identifiable "words" we could form with, say, 4 e's and 4 h's'

And this is given by    8!  / (4! * 4!)  =  70

There are only 2 ways to draw alternate colors  .... BWBWBW.......etc.    or   WBWBWB......etc.

So.....the probability of alternating colors on the draws is just  2 / 70   or 1 / 35

If this isn't correct......maybe wait until Melody comes on later.....

 

  

CPhill May 6, 2015
 #2
avatar+906 
+3

?

probability?

 May 6, 2015
 #3
avatar+1836 
+1

Even though you might think others are better than you, you are still very intelligent. (Not putting the others down, just saying that you are very smart)

 May 6, 2015
 #4
avatar+1314 
+3

dunno, 50? or 70

 May 6, 2015
 #5
avatar+118696 
+11

 

$probthattheyalternate$=2(48×47×36×35×24×23×12×11)=2×(4!)28!

 

 2×4!28!=135=0.0285714285714286

 

I times it by 2 because either the black can come first OR the white can come first  

 

CPhill and I got the same answer - how about that !

CPhill's logic is different from mine but both make perfect sense to me :)

 May 6, 2015
 #6
avatar+130466 
+11

Hey......Melody and I got the same answer to a probability problem......!!!!!

 

 

  

 May 6, 2015
 #7
avatar+118696 
+6

YES it is proof - miracles really can happen !!   LOL

 May 7, 2015

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