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In an animal shelter with 30 animals, each of which is either a cat or a dog, 12 out of 15 dogs have long fur and 11 out of 15 cats have long fur. What is the probability that in a randomly selected group of five animals from the shelter, there will be two long-furred dogs and three long-furred cats? Express your answer as a decimal to the nearest thousandth.

 

I got (5C2)*((12C2)+(11C3))/(30C5) but I'm not sure because that probability seems unreasonably low so it would be nice if anyone was willing to check. Thanks!

 Feb 21, 2023
edited by idontknowhowtodivide  Feb 21, 2023
 #1
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That looks right to me!

 Feb 22, 2023
 #2
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This is how I would look at it.

Choose 2 dogs from  12 long haired ones   and    Choose 3 cats from ll long haireds ones 

and put it over  5 animals from a total of 30 animals

 

= ( 12C2 * 11C3 ) / 30C5    =   66*165 / 142506  =  10890 / 142506 = 605 / 7917   = approx 7.6%

That sounds ok to me.

 

 

I do not know why you multiplied that by 5C2

 Feb 22, 2023
 #3
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5 choose 2 is the number of ways to pick the order of the ways you pick a dog and cat, but now I realize that's probably wrong.

idontknowhowtodivide  Feb 22, 2023
 #4
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ok now I understand what you have done.

In this case order does not count.  I am glad you worked that out for yourself :)

Melody  Feb 23, 2023
 #5
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Now I understand how to do it, thanks for the help Melody

idontknowhowtodivide  Feb 23, 2023

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