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An urn contains 7 white marbles and 5 blue marbles. Four marbles are selected without replcament. Find each probablitiy.

 

1. P (4 white or 4 blue)

 

2. P (exactly 3 white)

 

3. P ( at least 3 white)
 Jun 3, 2014

Best Answer 

 #1
avatar+130511 
+8

I'm not great at probability.....but  I'll see what I can do for you......

First off, the number of total outcomes possible from drawing 4 b***s out of 12 is just C(12,4) = 495......this will be the denominator in our answers......

P(4white or 4blue) = P(4white) + P(4blue) - P(4 white and 4 blue)

The last thing = 0  (We can't draw 4 white ones and 4 blue ones at the same time)

P(4white)  = choose any 4 of the 7 white ones = C(7,4) = 35

P(4blue) = choose any 4 from the 5 blue ones = C(5,4) = 5

So we have   (35 + 5)/495 = 40/495 = 8/99

---------------------------------------------------------------------------------------------------

P(3white).....choose 3 of the 7 white ones and 1 of the 5 blue ones =

C(7,3) * C(5,1) = 175.....so we have

175/495 = 35/99

----------------------------------------------------------------------------------------------------

P(at least 3 white) = P(3white) + P(4white) =

(175 + 35)/ 495 = 210/495 = 42/99 = 14/33

----------------------------------------------------------------------------------------------------

If another answerer sees any mistakes....feel free to correct me !!

 Jun 3, 2014
 #1
avatar+130511 
+8
Best Answer

I'm not great at probability.....but  I'll see what I can do for you......

First off, the number of total outcomes possible from drawing 4 b***s out of 12 is just C(12,4) = 495......this will be the denominator in our answers......

P(4white or 4blue) = P(4white) + P(4blue) - P(4 white and 4 blue)

The last thing = 0  (We can't draw 4 white ones and 4 blue ones at the same time)

P(4white)  = choose any 4 of the 7 white ones = C(7,4) = 35

P(4blue) = choose any 4 from the 5 blue ones = C(5,4) = 5

So we have   (35 + 5)/495 = 40/495 = 8/99

---------------------------------------------------------------------------------------------------

P(3white).....choose 3 of the 7 white ones and 1 of the 5 blue ones =

C(7,3) * C(5,1) = 175.....so we have

175/495 = 35/99

----------------------------------------------------------------------------------------------------

P(at least 3 white) = P(3white) + P(4white) =

(175 + 35)/ 495 = 210/495 = 42/99 = 14/33

----------------------------------------------------------------------------------------------------

If another answerer sees any mistakes....feel free to correct me !!

CPhill Jun 3, 2014
 #2
avatar+118723 
0

Hi Chris,

I have not done these questions thoroughly but your answers look alright to me.  

 Jun 4, 2014

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