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December 9th, 2018, 09:51 PM  #1 
Newbie Joined: Sep 2008 Posts: 7 Thanks: 0  Possibilities of drawing balls?
I have a bag with 100 balls, 62 of them are red and the others 38 are white. if I take 4 of them at random, what are the probabilities of all of them being the white ones? Regards Last edited by sergio1971; December 9th, 2018 at 10:36 PM. 
December 9th, 2018, 10:56 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198 
$\dfrac{\dbinom{62}{0}\dbinom{38}{4}}{\dbinom{100} {4}} = \dfrac{703}{37345}$ 
December 10th, 2018, 02:32 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,663 Thanks: 649 
Shorter formula $\frac{38\times 37\times 36\times 35}{100\times 99\times 98 \times 97}$

January 5th, 2019, 12:42 AM  #4 
Newbie Joined: Sep 2008 Posts: 7 Thanks: 0 
thanks for your reply, in my previous post I should have pointed out that every time you take a ball, your notice its color and put in again in the bag so every time you reach for a ball there are 100 inside. can someone give me a correct answer ?. Thanks for your help

January 5th, 2019, 01:15 AM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198  Quote:
with parameters $n=4,~p=\dfrac{38}{100}$ $P[\text{all 4 chosen balls are white}]=\left(\dfrac{38}{100}\right)^4 = \dfrac{2085136}{100000000} = \dfrac{130321}{6250000}$  

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